-1.5x^2+93x-1260=180

Solution for -1.5x^2+93x-1260=180 equation:

-1.5x^2+93x-1260=180

We move all terms to the left:

-1.5x^2+93x-1260-(180)=0

We add all the numbers together, and all the variables

-1.5x^2+93x-1440=0

a = -1.5; b = 93; c = -1440;
Δ = b2-4ac
Δ = 932-4·(-1.5)·(-1440)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(93)-3}{2*-1.5}=\frac{-96}{-3}
=+32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(93)+3}{2*-1.5}=\frac{-90}{-3}
=+30
$