13-6x(2x-6)=-5

Solution for 13-6x(2x-6)=-5 equation:

13-6x(2x-6)=-5

We move all terms to the left:

13-6x(2x-6)-(-5)=0

We add all the numbers together, and all the variables

-6x(2x-6)+18=0

We multiply parentheses

-12x^2+36x+18=0

a = -12; b = 36; c = +18;
Δ = b2-4ac
Δ = 362-4·(-12)·18
Δ = 2160
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:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{15}}{2*-12}=\frac{-36-12\sqrt{15}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{15}}{2*-12}=\frac{-36+12\sqrt{15}}{-24}
$