-5x^2-6x=-3

Solution for -5x^2-6x=-3 equation:

-5x^2-6x=-3

We move all terms to the left:

-5x^2-6x-(-3)=0

We add all the numbers together, and all the variables

-5x^2-6x+3=0

a = -5; b = -6; c = +3;
Δ = b2-4ac
Δ = -62-4·(-5)·3
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{6}}{2*-5}=\frac{6-4\sqrt{6}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{6}}{2*-5}=\frac{6+4\sqrt{6}}{-10}
$