3x^2+9x-54=54

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

3x^2+9x-54=54

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x^2+9x-108=0

a = 3; b = 9; c = -108;
Δ = b2-4ac
Δ = 92-4·3·(-108)
Δ = 1377
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:

$\sqrt{\Delta}=\sqrt{1377}=\sqrt{81*17}=\sqrt{81}*\sqrt{17}=9\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9\sqrt{17}}{2*3}=\frac{-9-9\sqrt{17}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9\sqrt{17}}{2*3}=\frac{-9+9\sqrt{17}}{6}
$