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

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

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

We move all terms to the left:

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

We multiply parentheses ..

4(+4x^2-7x-28x+49)-(x(4x-8)-156)=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 multiply parentheses

16x^2-28x-112x-(4x^2-8x-156)+196=0

We get rid of parentheses

16x^2-4x^2-28x-112x+8x+156+196=0

We add all the numbers together, and all the variables

12x^2-132x+352=0

a = 12; b = -132; c = +352;
Δ = b2-4ac
Δ = -1322-4·12·352
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-4\sqrt{33}}{2*12}=\frac{132-4\sqrt{33}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+4\sqrt{33}}{2*12}=\frac{132+4\sqrt{33}}{24}
$