90x=-0.2x^2-10x-2500

Solution for 90x=-0.2x^2-10x-2500 equation:

90x=-0.2x^2-10x-2500

We move all terms to the left:

90x-(-0.2x^2-10x-2500)=0

We get rid of parentheses

0.2x^2+10x+90x+2500=0

We add all the numbers together, and all the variables

0.2x^2+100x+2500=0

a = 0.2; b = 100; c = +2500;
Δ = b2-4ac
Δ = 1002-4·0.2·2500
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-40\sqrt{5}}{2*0.2}=\frac{-100-40\sqrt{5}}{0.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+40\sqrt{5}}{2*0.2}=\frac{-100+40\sqrt{5}}{0.4}
$