4(x-7)(x+7)=x(4x-8)-156

Solution for 4(x-7)(x+7)=x(4x-8)-156 equation:

4(x-7)(x+7)=x(4x-8)-156

We move all terms to the left:

4(x-7)(x+7)-(x(4x-8)-156)=0

We use the square of the difference formula

x^2-(x(4x-8)-156)-49=0


We calculate terms in parentheses: -(x(4x-8)-156), so:

x(4x-8)-156

We multiply parentheses

4x^2-8x-156

Back to the equation:

-(4x^2-8x-156)


We get rid of parentheses

x^2-4x^2+8x+156-49=0

We add all the numbers together, and all the variables

-3x^2+8x+107=0

a = -3; b = 8; c = +107;
Δ = b2-4ac
Δ = 82-4·(-3)·107
Δ = 1348
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1348}=\sqrt{4*337}=\sqrt{4}*\sqrt{337}=2\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{337}}{2*-3}=\frac{-8-2\sqrt{337}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{337}}{2*-3}=\frac{-8+2\sqrt{337}}{-6}
$