54x^2+12x=540

Solution for 54x^2+12x=540 equation:

54x^2+12x=540

We move all terms to the left:

54x^2+12x-(540)=0

a = 54; b = 12; c = -540;
Δ = b2-4ac
Δ = 122-4·54·(-540)
Δ = 116784
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:

$\sqrt{\Delta}=\sqrt{116784}=\sqrt{144*811}=\sqrt{144}*\sqrt{811}=12\sqrt{811}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{811}}{2*54}=\frac{-12-12\sqrt{811}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{811}}{2*54}=\frac{-12+12\sqrt{811}}{108}
$