9x^2+144x+54=0

Solution for 9x^2+144x+54=0 equation:

9x^2+144x+54=0

a = 9; b = 144; c = +54;
Δ = b2-4ac
Δ = 1442-4·9·54
Δ = 18792
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:

$\sqrt{\Delta}=\sqrt{18792}=\sqrt{324*58}=\sqrt{324}*\sqrt{58}=18\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-18\sqrt{58}}{2*9}=\frac{-144-18\sqrt{58}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+18\sqrt{58}}{2*9}=\frac{-144+18\sqrt{58}}{18}
$