50,000=20x^2+360x+18,000

Solution for 50,000=20x^2+360x+18,000 equation:

50.000=20x^2+360x+18.000

We move all terms to the left:

50.000-(20x^2+360x+18.000)=0

We add all the numbers together, and all the variables

-(20x^2+360x+18.000)+50=0

We get rid of parentheses

-20x^2-360x-18.000+50=0

We add all the numbers together, and all the variables

-20x^2-360x+32=0

a = -20; b = -360; c = +32;
Δ = b2-4ac
Δ = -3602-4·(-20)·32
Δ = 132160
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:

$\sqrt{\Delta}=\sqrt{132160}=\sqrt{64*2065}=\sqrt{64}*\sqrt{2065}=8\sqrt{2065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-8\sqrt{2065}}{2*-20}=\frac{360-8\sqrt{2065}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+8\sqrt{2065}}{2*-20}=\frac{360+8\sqrt{2065}}{-40}
$