144=9x^2+54x

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

144=9x^2+54x

We move all terms to the left:

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

We get rid of parentheses

-9x^2-54x+144=0

a = -9; b = -54; c = +144;
Δ = b2-4ac
Δ = -542-4·(-9)·144
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-90}{2*-9}=\frac{-36}{-18}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+90}{2*-9}=\frac{144}{-18}
=-8
$