x^2-26x=165

Solution for x^2-26x=165 equation:

x^2-26x=165

We move all terms to the left:

x^2-26x-(165)=0

a = 1; b = -26; c = -165;
Δ = b2-4ac
Δ = -262-4·1·(-165)
Δ = 1336
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:

$\sqrt{\Delta}=\sqrt{1336}=\sqrt{4*334}=\sqrt{4}*\sqrt{334}=2\sqrt{334}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{334}}{2*1}=\frac{26-2\sqrt{334}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{334}}{2*1}=\frac{26+2\sqrt{334}}{2}
$