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

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

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

We move all terms to the left:

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

We multiply parentheses ..

4(+4x^2-8x-28x+56)-(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^2-32x-112x-(4x^2-8x-156)+224=0

We get rid of parentheses

16x^2-4x^2-32x-112x+8x+156+224=0

We add all the numbers together, and all the variables

12x^2-136x+380=0

a = 12; b = -136; c = +380;
Δ = b2-4ac
Δ = -1362-4·12·380
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-136)-16}{2*12}=\frac{120}{24}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-136)+16}{2*12}=\frac{152}{24}
=6+1/3
$