4x^2-2=-3x

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

4x^2-2=-3x

We move all terms to the left:

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

We get rid of parentheses

4x^2+3x-2=0

a = 4; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·4·(-2)
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*4}=\frac{-3-\sqrt{41}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{41}}{2*4}=\frac{-3+\sqrt{41}}{8}
$