-6x(x+1)+18=-24

Solution for -6x(x+1)+18=-24 equation:

-6x(x+1)+18=-24

We move all terms to the left:

-6x(x+1)+18-(-24)=0

We add all the numbers together, and all the variables

-6x(x+1)+42=0

We multiply parentheses

-6x^2-6x+42=0

a = -6; b = -6; c = +42;
Δ = b2-4ac
Δ = -62-4·(-6)·42
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{29}}{2*-6}=\frac{6-6\sqrt{29}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{29}}{2*-6}=\frac{6+6\sqrt{29}}{-12}
$