3x+15=2x^2+4x+2

Solution for 3x+15=2x^2+4x+2 equation:

3x+15=2x^2+4x+2

We move all terms to the left:

3x+15-(2x^2+4x+2)=0

We get rid of parentheses

-2x^2+3x-4x-2+15=0

We add all the numbers together, and all the variables

-2x^2-1x+13=0

a = -2; b = -1; c = +13;
Δ = b2-4ac
Δ = -12-4·(-2)·13
Δ = 105
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{-(-1)-\sqrt{105}}{2*-2}=\frac{1-\sqrt{105}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{105}}{2*-2}=\frac{1+\sqrt{105}}{-4}
$