X^2+23x+15=5x-30

Solution for X^2+23x+15=5x-30 equation:

X^2+23X+15=5X-30

We move all terms to the left:

X^2+23X+15-(5X-30)=0

We get rid of parentheses

X^2+23X-5X+30+15=0

We add all the numbers together, and all the variables

X^2+18X+45=0

a = 1; b = 18; c = +45;
Δ = b2-4ac
Δ = 182-4·1·45
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-12}{2*1}=\frac{-30}{2}
=-15
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+12}{2*1}=\frac{-6}{2}
=-3
$