X^2-15x+15=2

Solution for X^2-15x+15=2 equation:

X^2-15X+15=2

We move all terms to the left:

X^2-15X+15-(2)=0

We add all the numbers together, and all the variables

X^2-15X+13=0

a = 1; b = -15; c = +13;
Δ = b2-4ac
Δ = -152-4·1·13
Δ = 173
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{173}}{2*1}=\frac{15-\sqrt{173}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{173}}{2*1}=\frac{15+\sqrt{173}}{2}
$