(6x)(x+13)=90

Solution for (6x)(x+13)=90 equation:

(6x)(x+13)=90

We move all terms to the left:

(6x)(x+13)-(90)=0

We multiply parentheses

6x^2+78x-90=0

a = 6; b = 78; c = -90;
Δ = b2-4ac
Δ = 782-4·6·(-90)
Δ = 8244
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:

$\sqrt{\Delta}=\sqrt{8244}=\sqrt{36*229}=\sqrt{36}*\sqrt{229}=6\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-6\sqrt{229}}{2*6}=\frac{-78-6\sqrt{229}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+6\sqrt{229}}{2*6}=\frac{-78+6\sqrt{229}}{12}
$