3x^2=54x+12

Solution for 3x^2=54x+12 equation:

3x^2=54x+12

We move all terms to the left:

3x^2-(54x+12)=0

We get rid of parentheses

3x^2-54x-12=0

a = 3; b = -54; c = -12;
Δ = b2-4ac
Δ = -542-4·3·(-12)
Δ = 3060
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:

$\sqrt{\Delta}=\sqrt{3060}=\sqrt{36*85}=\sqrt{36}*\sqrt{85}=6\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{85}}{2*3}=\frac{54-6\sqrt{85}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{85}}{2*3}=\frac{54+6\sqrt{85}}{6}
$