13x(x-6)=-108

Solution for 13x(x-6)=-108 equation:

13x(x-6)=-108

We move all terms to the left:

13x(x-6)-(-108)=0

We add all the numbers together, and all the variables

13x(x-6)+108=0

We multiply parentheses

13x^2-78x+108=0

a = 13; b = -78; c = +108;
Δ = b2-4ac
Δ = -782-4·13·108
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-6\sqrt{13}}{2*13}=\frac{78-6\sqrt{13}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+6\sqrt{13}}{2*13}=\frac{78+6\sqrt{13}}{26}
$