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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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