-20x^2+1000x+12000=16500

Solution for -20x^2+1000x+12000=16500 equation:

-20x^2+1000x+12000=16500

We move all terms to the left:

-20x^2+1000x+12000-(16500)=0

We add all the numbers together, and all the variables

-20x^2+1000x-4500=0

a = -20; b = 1000; c = -4500;
Δ = b2-4ac
Δ = 10002-4·(-20)·(-4500)
Δ = 640000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{640000}=800$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1000)-800}{2*-20}=\frac{-1800}{-40}
=+45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1000)+800}{2*-20}=\frac{-200}{-40}
=+5
$