Given that x^2:(3x+5) = 1:2 Find the possible values of x?

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answers:
Jim Moor say: x²:(3x+5) = 1:2
x²/(3x+5) = 1/2
multiply by 2(3x+5) to both sides to maintain equality
2x² = 3x +5
2 x² - 3 x - 5 = 0
Factor, Complete the Square or use QF:

The left hand side factors into a product with two terms:
(x + 1) (2 x - 5) = 0

Split into two equations:
x + 1 = 0 or 2 x - 5 = 0

Subtract 1 from both sides:
x = -1

2 x - 5 = 0
Add 5 to both sides:

x = -1 or 2 x = 5

Divide both sides by 2:

Answer: x = -1 or x = 5/2
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alex say: x^2/(3x + 5) = 1/2
solve for x
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Mike G say: 2x^2-3x-5 = 0
(2x-5)(x+1) = 0
x = -1 or 2.5
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Iggy Rocko say: x^2/(3x + 5) = 1/2
2x^2 = 3x + 5
2x^2 - 3x - 5 = 0
(2x - 5)(x + 1) = 0
x = 5/2 or x = -1
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Como say: --
x² / (3x + 5) = 1/2
2x² = 3x + 5
2x² - 3x - 5 = 0
( 2x - 5 ) ( x + 1 ) = 0
x = 5/2 , x = - 1
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Puzzling say: Change the ratio into divisions:
x² / (3x + 5) = 1 / 2

Cross multiply:
2x² = 3x + 5

Get everything on one side:
2x² - 3x - 5 = 0

Factor:
(2x - 5)(x + 1) = 0

By the zero product rule, if ab = 0, then a=0 or b=0:
2x - 5 = 0
2x = 5
x = 5/2
x = 2½
or
x + 1 = 0
x = -1

Double-check both answers make sense:
(2.5)² = 6.25 and 3(2.5) + 5 = 12.5
6.25 / 12.5 = 1 / 2

(-1)² = 1 and 3(-1) + 5 = 2
1 / 2 = 1 / 2

Answer:
x = 2.5 or x = -1
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Captain Matticus, LandPiratesInc say: 2 * x^2 = 1 * (3x + 5)
2x^2 - 3x - 5 = 0
x = (3 +/- sqrt(9 + 40)) / 4
x = (3 +/- 7) / 4
x = 10/4 , -4/4
x = 2.5 , -1

2.5^2 = 6.25
3 * 2.5 + 5 = 7.5 + 5 = 12.5

6.25 / 12.5 = 1/2

(-1)^2 / (3 * (-1) + 5) =>
1 / (-3 + 5) =>
1/2

Both work
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