x(x-26)=180

Solution for x(x-26)=180 equation:

x(x-26)=180

We move all terms to the left:

x(x-26)-(180)=0

We multiply parentheses

x^2-26x-180=0

a = 1; b = -26; c = -180;
Δ = b2-4ac
Δ = -262-4·1·(-180)
Δ = 1396
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:

$\sqrt{\Delta}=\sqrt{1396}=\sqrt{4*349}=\sqrt{4}*\sqrt{349}=2\sqrt{349}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{349}}{2*1}=\frac{26-2\sqrt{349}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{349}}{2*1}=\frac{26+2\sqrt{349}}{2}
$