-6x(x+5)-45=3-36

Solution for -6x(x+5)-45=3-36 equation:

-6x(x+5)-45=3-36

We move all terms to the left:

-6x(x+5)-45-(3-36)=0

We add all the numbers together, and all the variables

-6x(x+5)-45-(-33)=0

We add all the numbers together, and all the variables

-6x(x+5)-12=0

We multiply parentheses

-6x^2-30x-12=0

a = -6; b = -30; c = -12;
Δ = b2-4ac
Δ = -302-4·(-6)·(-12)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{17}}{2*-6}=\frac{30-6\sqrt{17}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{17}}{2*-6}=\frac{30+6\sqrt{17}}{-12}
$