X^2-26x=60-x^2

Solution for X^2-26x=60-x^2 equation:

X^2-26X=60-X^2

We move all terms to the left:

X^2-26X-(60-X^2)=0

We get rid of parentheses

X^2+X^2-26X-60=0

We add all the numbers together, and all the variables

2X^2-26X-60=0

a = 2; b = -26; c = -60;
Δ = b2-4ac
Δ = -262-4·2·(-60)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-34}{2*2}=\frac{-8}{4}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+34}{2*2}=\frac{60}{4}
=15
$