3x+15=2x^2+2x

Solution for 3x+15=2x^2+2x equation:

3x+15=2x^2+2x

We move all terms to the left:

3x+15-(2x^2+2x)=0

We get rid of parentheses

-2x^2+3x-2x+15=0

We add all the numbers together, and all the variables

-2x^2+x+15=0

a = -2; b = 1; c = +15;
Δ = b2-4ac
Δ = 12-4·(-2)·15
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*-2}=\frac{10}{-4}
=-2+1/2
$