x^2=15x-30

Solution for x^2=15x-30 equation:

x^2=15x-30

We move all terms to the left:

x^2-(15x-30)=0

We get rid of parentheses

x^2-15x+30=0

a = 1; b = -15; c = +30;
Δ = b2-4ac
Δ = -152-4·1·30
Δ = 105
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{105}}{2*1}=\frac{15-\sqrt{105}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{105}}{2*1}=\frac{15+\sqrt{105}}{2}
$