6x(x+8)=60

Solution for 6x(x+8)=60 equation:

6x(x+8)=60

We move all terms to the left:

6x(x+8)-(60)=0

We multiply parentheses

6x^2+48x-60=0

a = 6; b = 48; c = -60;
Δ = b2-4ac
Δ = 482-4·6·(-60)
Δ = 3744
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:

$\sqrt{\Delta}=\sqrt{3744}=\sqrt{144*26}=\sqrt{144}*\sqrt{26}=12\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-12\sqrt{26}}{2*6}=\frac{-48-12\sqrt{26}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+12\sqrt{26}}{2*6}=\frac{-48+12\sqrt{26}}{12}
$