x(52-4x)=99

Solution for x(52-4x)=99 equation:

x(52-4x)=99

We move all terms to the left:

x(52-4x)-(99)=0

We add all the numbers together, and all the variables

x(-4x+52)-99=0

We multiply parentheses

-4x^2+52x-99=0

a = -4; b = 52; c = -99;
Δ = b2-4ac
Δ = 522-4·(-4)·(-99)
Δ = 1120
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:

$\sqrt{\Delta}=\sqrt{1120}=\sqrt{16*70}=\sqrt{16}*\sqrt{70}=4\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{70}}{2*-4}=\frac{-52-4\sqrt{70}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{70}}{2*-4}=\frac{-52+4\sqrt{70}}{-8}
$