x^2=30+13x

Solution for x^2=30+13x equation:

x^2=30+13x

We move all terms to the left:

x^2-(30+13x)=0

We add all the numbers together, and all the variables

x^2-(13x+30)=0

We get rid of parentheses

x^2-13x-30=0

a = 1; b = -13; c = -30;
Δ = b2-4ac
Δ = -132-4·1·(-30)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-17}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+17}{2*1}=\frac{30}{2}
=15
$