x^2-57x=108

Solution for x^2-57x=108 equation:

x^2-57x=108

We move all terms to the left:

x^2-57x-(108)=0

a = 1; b = -57; c = -108;
Δ = b2-4ac
Δ = -572-4·1·(-108)
Δ = 3681
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:

$\sqrt{\Delta}=\sqrt{3681}=\sqrt{9*409}=\sqrt{9}*\sqrt{409}=3\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-3\sqrt{409}}{2*1}=\frac{57-3\sqrt{409}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+3\sqrt{409}}{2*1}=\frac{57+3\sqrt{409}}{2}
$