20x^2+290x+600=90000

Solution for 20x^2+290x+600=90000 equation:

20x^2+290x+600=90000

We move all terms to the left:

20x^2+290x+600-(90000)=0

We add all the numbers together, and all the variables

20x^2+290x-89400=0

a = 20; b = 290; c = -89400;
Δ = b2-4ac
Δ = 2902-4·20·(-89400)
Δ = 7236100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7236100}=2690$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(290)-2690}{2*20}=\frac{-2980}{40}
=-74+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(290)+2690}{2*20}=\frac{2400}{40}
=60
$