-2a^2=2a-3=-4a

Solution for -2a^2=2a-3=-4a equation:

-2a^2=2a-3=-4a

We move all terms to the left:

-2a^2-(2a-3)=0

We get rid of parentheses

-2a^2-2a+3=0

a = -2; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-2)·3
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{7}}{2*-2}=\frac{2-2\sqrt{7}}{-4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{7}}{2*-2}=\frac{2+2\sqrt{7}}{-4}
$