x^2-20x=18

Solution for x^2-20x=18 equation:

x^2-20x=18

We move all terms to the left:

x^2-20x-(18)=0

a = 1; b = -20; c = -18;
Δ = b2-4ac
Δ = -202-4·1·(-18)
Δ = 472
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:

$\sqrt{\Delta}=\sqrt{472}=\sqrt{4*118}=\sqrt{4}*\sqrt{118}=2\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{118}}{2*1}=\frac{20-2\sqrt{118}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{118}}{2*1}=\frac{20+2\sqrt{118}}{2}
$