x(x-4)=117

Solution for x(x-4)=117 equation:

x(x-4)=117

We move all terms to the left:

x(x-4)-(117)=0

We multiply parentheses

x^2-4x-117=0

a = 1; b = -4; c = -117;
Δ = b2-4ac
Δ = -42-4·1·(-117)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-22}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+22}{2*1}=\frac{26}{2}
=13
$