6x^2+60x=54

Solution for 6x^2+60x=54 equation:

6x^2+60x=54

We move all terms to the left:

6x^2+60x-(54)=0

a = 6; b = 60; c = -54;
Δ = b2-4ac
Δ = 602-4·6·(-54)
Δ = 4896
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:

$\sqrt{\Delta}=\sqrt{4896}=\sqrt{144*34}=\sqrt{144}*\sqrt{34}=12\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-12\sqrt{34}}{2*6}=\frac{-60-12\sqrt{34}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+12\sqrt{34}}{2*6}=\frac{-60+12\sqrt{34}}{12}
$