15+2x=8x^2-12x

Solution for 15+2x=8x^2-12x equation:

15+2x=8x^2-12x

We move all terms to the left:

15+2x-(8x^2-12x)=0

We get rid of parentheses

-8x^2+2x+12x+15=0

We add all the numbers together, and all the variables

-8x^2+14x+15=0

a = -8; b = 14; c = +15;
Δ = b2-4ac
Δ = 142-4·(-8)·15
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-26}{2*-8}=\frac{-40}{-16}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+26}{2*-8}=\frac{12}{-16}
=-3/4
$