x2+23x+15=5x-30

Solution for x2+23x+15=5x-30 equation:

x2+23x+15=5x-30

We move all terms to the left:

x2+23x+15-(5x-30)=0

We add all the numbers together, and all the variables

x^2+23x-(5x-30)+15=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
$