144000+80x=500x-0.1x^2

Solution for 144000+80x=500x-0.1x^2 equation:

144000+80x=500x-0.1x^2

We move all terms to the left:

144000+80x-(500x-0.1x^2)=0

We get rid of parentheses

0.1x^2-500x+80x+144000=0

We add all the numbers together, and all the variables

0.1x^2-420x+144000=0

a = 0.1; b = -420; c = +144000;
Δ = b2-4ac
Δ = -4202-4·0.1·144000
Δ = 118800
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:

$\sqrt{\Delta}=\sqrt{118800}=\sqrt{3600*33}=\sqrt{3600}*\sqrt{33}=60\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-60\sqrt{33}}{2*0.1}=\frac{420-60\sqrt{33}}{0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+60\sqrt{33}}{2*0.1}=\frac{420+60\sqrt{33}}{0.2}
$