-2x^2+4=3x

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

-2x^2+4=3x

We move all terms to the left:

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

a = -2; b = -3; c = +4;
Δ = b2-4ac
Δ = -32-4·(-2)·4
Δ = 41
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{-(-3)-\sqrt{41}}{2*-2}=\frac{3-\sqrt{41}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{41}}{2*-2}=\frac{3+\sqrt{41}}{-4}
$