x^2-15x=-25

Solution for x^2-15x=-25 equation:

x^2-15x=-25

We move all terms to the left:

x^2-15x-(-25)=0

We add all the numbers together, and all the variables

x^2-15x+25=0

a = 1; b = -15; c = +25;
Δ = b2-4ac
Δ = -152-4·1·25
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{5}}{2*1}=\frac{15-5\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{5}}{2*1}=\frac{15+5\sqrt{5}}{2}
$