-3x^2-23x=-40

Solution for -3x^2-23x=-40 equation:

-3x^2-23x=-40

We move all terms to the left:

-3x^2-23x-(-40)=0

We add all the numbers together, and all the variables

-3x^2-23x+40=0

a = -3; b = -23; c = +40;
Δ = b2-4ac
Δ = -232-4·(-3)·40
Δ = 1009
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{-(-23)-\sqrt{1009}}{2*-3}=\frac{23-\sqrt{1009}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{1009}}{2*-3}=\frac{23+\sqrt{1009}}{-6}
$