9x^2-54=144

Solution for 9x^2-54=144 equation:

9x^2-54=144

We move all terms to the left:

9x^2-54-(144)=0

We add all the numbers together, and all the variables

9x^2-198=0

a = 9; b = 0; c = -198;
Δ = b2-4ac
Δ = 02-4·9·(-198)
Δ = 7128
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:

$\sqrt{\Delta}=\sqrt{7128}=\sqrt{324*22}=\sqrt{324}*\sqrt{22}=18\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{22}}{2*9}=\frac{0-18\sqrt{22}}{18}
=-\frac{18\sqrt{22}}{18}
=-\sqrt{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{22}}{2*9}=\frac{0+18\sqrt{22}}{18}
=\frac{18\sqrt{22}}{18}
=\sqrt{22}
$