x^2-12x+15=2x-10

Solution for x^2-12x+15=2x-10 equation:

x^2-12x+15=2x-10

We move all terms to the left:

x^2-12x+15-(2x-10)=0

We get rid of parentheses

x^2-12x-2x+10+15=0

We add all the numbers together, and all the variables

x^2-14x+25=0

a = 1; b = -14; c = +25;
Δ = b2-4ac
Δ = -142-4·1·25
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{6}}{2*1}=\frac{14-4\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{6}}{2*1}=\frac{14+4\sqrt{6}}{2}
$