112=8x(x-7)-8x^

Solution for 112=8x(x-7)-8x^ equation:

112=8x(x-7)-8x^

We move all terms to the left:

112-(8x(x-7)-8x^)=0


We calculate terms in parentheses: -(8x(x-7)-8x^), so:

8x(x-7)-8x^

We add all the numbers together, and all the variables

-8x+8x(x-7)

We multiply parentheses

8x^2-8x-56x

We add all the numbers together, and all the variables

8x^2-64x

Back to the equation:

-(8x^2-64x)


We get rid of parentheses

-8x^2+64x+112=0

a = -8; b = 64; c = +112;
Δ = b2-4ac
Δ = 642-4·(-8)·112
Δ = 7680
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:

$\sqrt{\Delta}=\sqrt{7680}=\sqrt{256*30}=\sqrt{256}*\sqrt{30}=16\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-16\sqrt{30}}{2*-8}=\frac{-64-16\sqrt{30}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+16\sqrt{30}}{2*-8}=\frac{-64+16\sqrt{30}}{-16}
$