-4x^2+3x=-6

Solution for -4x^2+3x=-6 equation:

-4x^2+3x=-6

We move all terms to the left:

-4x^2+3x-(-6)=0

We add all the numbers together, and all the variables

-4x^2+3x+6=0

a = -4; b = 3; c = +6;
Δ = b2-4ac
Δ = 32-4·(-4)·6
Δ = 105
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{105}}{2*-4}=\frac{-3-\sqrt{105}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{105}}{2*-4}=\frac{-3+\sqrt{105}}{-8}
$