X^2-18x=65

Solution for X^2-18x=65 equation:

X^2-18X=65

We move all terms to the left:

X^2-18X-(65)=0

a = 1; b = -18; c = -65;
Δ = b2-4ac
Δ = -182-4·1·(-65)
Δ = 584
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:

$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{146}}{2*1}=\frac{18-2\sqrt{146}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{146}}{2*1}=\frac{18+2\sqrt{146}}{2}
$