9x^2-3x=54

Solution for 9x^2-3x=54 equation:

9x^2-3x=54

We move all terms to the left:

9x^2-3x-(54)=0

a = 9; b = -3; c = -54;
Δ = b2-4ac
Δ = -32-4·9·(-54)
Δ = 1953
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:

$\sqrt{\Delta}=\sqrt{1953}=\sqrt{9*217}=\sqrt{9}*\sqrt{217}=3\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{217}}{2*9}=\frac{3-3\sqrt{217}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{217}}{2*9}=\frac{3+3\sqrt{217}}{18}
$