0=1.5x^2-52.5x-4500

Solution for 0=1.5x^2-52.5x-4500 equation:

0=1.5x^2-52.5x-4500

We move all terms to the left:

0-(1.5x^2-52.5x-4500)=0

We add all the numbers together, and all the variables

-(1.5x^2-52.5x-4500)=0

We get rid of parentheses

-1.5x^2+52.5x+4500=0

a = -1.5; b = 52.5; c = +4500;
Δ = b2-4ac
Δ = 52.52-4·(-1.5)·4500
Δ = 29756.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52.5)-\sqrt{29756.25}}{2*-1.5}=\frac{-52.5-\sqrt{29756.25}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52.5)+\sqrt{29756.25}}{2*-1.5}=\frac{-52.5+\sqrt{29756.25}}{-3}
$