x^2-12=-5x+18

Solution for x^2-12=-5x+18 equation:

x^2-12=-5x+18

We move all terms to the left:

x^2-12-(-5x+18)=0

We get rid of parentheses

x^2+5x-18-12=0

We add all the numbers together, and all the variables

x^2+5x-30=0

a = 1; b = 5; c = -30;
Δ = b2-4ac
Δ = 52-4·1·(-30)
Δ = 145
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{-(5)-\sqrt{145}}{2*1}=\frac{-5-\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{145}}{2*1}=\frac{-5+\sqrt{145}}{2}
$