100-23x(x+8)=28

Solution for 100-23x(x+8)=28 equation:

100-23x(x+8)=28

We move all terms to the left:

100-23x(x+8)-(28)=0

We add all the numbers together, and all the variables

-23x(x+8)+72=0

We multiply parentheses

-23x^2-184x+72=0

a = -23; b = -184; c = +72;
Δ = b2-4ac
Δ = -1842-4·(-23)·72
Δ = 40480
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:

$\sqrt{\Delta}=\sqrt{40480}=\sqrt{16*2530}=\sqrt{16}*\sqrt{2530}=4\sqrt{2530}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-184)-4\sqrt{2530}}{2*-23}=\frac{184-4\sqrt{2530}}{-46}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-184)+4\sqrt{2530}}{2*-23}=\frac{184+4\sqrt{2530}}{-46}
$