-8(x-44)x=7

Solution for -8(x-44)x=7 equation:

-8(x-44)x=7

We move all terms to the left:

-8(x-44)x-(7)=0

We multiply parentheses

-8x^2+352x-7=0

a = -8; b = 352; c = -7;
Δ = b2-4ac
Δ = 3522-4·(-8)·(-7)
Δ = 123680
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:

$\sqrt{\Delta}=\sqrt{123680}=\sqrt{16*7730}=\sqrt{16}*\sqrt{7730}=4\sqrt{7730}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(352)-4\sqrt{7730}}{2*-8}=\frac{-352-4\sqrt{7730}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(352)+4\sqrt{7730}}{2*-8}=\frac{-352+4\sqrt{7730}}{-16}
$