6x^2+108=54x

Solution for 6x^2+108=54x equation:

6x^2+108=54x

We move all terms to the left:

6x^2+108-(54x)=0

a = 6; b = -54; c = +108;
Δ = b2-4ac
Δ = -542-4·6·108
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-18}{2*6}=\frac{36}{12}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+18}{2*6}=\frac{72}{12}
=6
$