15x^2-3x-54=90

Solution for 15x^2-3x-54=90 equation:

15x^2-3x-54=90

We move all terms to the left:

15x^2-3x-54-(90)=0

We add all the numbers together, and all the variables

15x^2-3x-144=0

a = 15; b = -3; c = -144;
Δ = b2-4ac
Δ = -32-4·15·(-144)
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-93}{2*15}=\frac{-90}{30}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+93}{2*15}=\frac{96}{30}
=3+1/5
$