x=3x+15-2x^2

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

x=3x+15-2x^2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-2x-15=0

a = 2; b = -2; c = -15;
Δ = b2-4ac
Δ = -22-4·2·(-15)
Δ = 124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{31}}{2*2}=\frac{2-2\sqrt{31}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*2}=\frac{2+2\sqrt{31}}{4}
$