-4m^2-3m+3=-6

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

-4m^2-3m+3=-6

We move all terms to the left:

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

We add all the numbers together, and all the variables

-4m^2-3m+9=0

a = -4; b = -3; c = +9;
Δ = b2-4ac
Δ = -32-4·(-4)·9
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{17}}{2*-4}=\frac{3-3\sqrt{17}}{-8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{17}}{2*-4}=\frac{3+3\sqrt{17}}{-8}
$