Solve and find x-intersepts: 3x^2 - 7x - 5 = 0

Hi :

there are four ways to find this answer:

1) graph it

2) factor it

3) complete the square

4) the quadratic formula

I'll do it by number 4

x = (-b +/- sqt rt (b^2 - 4 ac))/2a

so

a= 3 ,b= -7 and c = -5

so

x = -(-7) +/- sq rt ((-7)^2 - 4(3)-5)/ 2(3)

Answer Number 1:

the plus half of the quadratic formula

x = (7 + sq rt (49- 4(3)-5) / 2(3)

x = ( 7 + sq rt(49 + 60)) / 6

x =( 7 + sq rt (109) )/ 6

x = ( 7 + 10.440306508911) / 6

x= 17.440306508911/ 6

x = 2.906717751485

Answer # 2

the minus half of the quadratic formula


x = - ( -7) - sq rt (-7^ 2 - 4 (3)-5)/ 2 (3)

x = (7 - sq rt (49- 4(3)-5) / 2(3)

x =( 7 - sq rt ( 49) - 4(3)-5)/ 2(3)

x = (7 - sq rt (49+ 60 ))/ 6

x = (7 - sq rt (109)) / 9

x = (7 - 10.440306508911)/ 6

x = -3. 440306508911/ 6

x = - 0.573384418152

soultion ( x = - 0.573384418152 , or x = 2.906717751485 )

proof or check

when x = 2.906717751485

3x^2 - 7x - 5 = 0 - original equation

3( 2.906717751485)^ 2 - 7( 2.906717751485 ) - 5 = 0 - plugging x with 2.906717751485

3(8.449008086799) - 7(2.906717751485 ) - 5 = 0 - solving the square of 2.906717751485

25.347024260396 - 20.347024260396 - 5 = 0 - multiplication

5 - 5 = 0 - Subtraction

0 = 0 - Subtraction

it checks and equals

answer # 2

when x = - 0.573384418152

3x^2 - 7x - 5 = 0 - original equation

3(- 0.573384418152 )^ 2 - 7(- 0.573384418152 ) - 5 = 0 - plugging x with - 0.573384418152


3( 0.328769690979 ) - 7(- 0.573384418152 ) - 5 = 0 - solving the square of - 0.573384418152

( 0.986309072937 ) + 4.013690927063 - 5 = 0 - multiplication

5 - 5 = 0 - Addition

0 = 0 - subtraction

it checks and equals

I hope this helps.

cant do it by trinomials so had to use quadratics.
rounded: -0.6 and 2.9
hope i helped