4x² - 12x = 312. How do i find x

4x^2-12x = 312
4x^2-12x-312 = 0
4(x^2-3x-78) = 0
x^2-3x-78 = 0/4
x^2-3x-78 = 0

Quadratic Formula:
x = -b+-√(b^2-4ac) / 2a
In this problem: a=1, b=-3, and c=-78.

x = -(-3)+-√((-3)^2-4(1)(-78)) / 2(1)
x = 3+-√(9+312) / 2
x = 3+-√321 / 2

Answer: x=(3+√321)/2 or x=(3-√321)/2
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Additional Problem:

A = (1/2)bh
156 = (1/2)(2x)(x-3)
156 = x(x-3)
156 = x^2-3x
0 = x^2-3x-156

x = -b+-√(b^2-4ac) / 2a
x = -(-3)+-√((-3)^2-4(1)(-156)) / 2(1)
x = 3+-√(9+624) / 2
x = 3+-√633 / 2
x=(3+√633)/2 or x=(3-√633)/2
However, x=(3-√633)/2 would give you a negative length (which is not possible), for the base and height, so eliminate that.

Answer: x=(3+√633)/2

Divide everything by 4:
x² - 3x = 78
x² - 3x - 78 = 0

From here, you could use the quadratic equation. Just for the exercise, here's how to "complete the square". I'd start from the previous step:
x² - 3x = 78
x² - 3x + 9/4 = 78 + 9/4
(x - 3/2)² = 321/4

Take the square roots of both sides:
x - 3/2 = (±√321)/2
x = 3/2 ± (√321)/2

This looks neater as:
x = (3 ± √321)/2

Decimal approximations (to two places):
x = -7.46, 10.46

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Area of a triangle = (base * height)/2

x(x - 3) = 156
x² - 3x = 156

Completing the square, as above:
x² - 3x + 9/4 = 156 + 9/4
(x - 3/2)² = 633/4
x - 3/2 = (±√633)/2
x = (3 ± √633)/2

We're looking for x to be a positive number, so x = (3 + √633)/2

Decimal approximation (to two places):
x = 14.08 cm

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First, get rid of the 4. Divide thru by 4 to obtain, x^2 - 3x - 78 = 0
Then, apply the quadratic formula: x = (3 +- sqrt(321))/2

how did you do the squared character is the real question.

4x² - 12x = 312

4x² - 12x - 312

4(x^2 - 3x - 78)= 0

x^2 - 3x - 78

x(x - 3) = 78

1. x = 78

2. x - 3 = 0

x = 3

TI89