x^2+20x=-2x^2+10x+3000

Solution for x^2+20x=-2x^2+10x+3000 equation:

x^2+20x=-2x^2+10x+3000

We move all terms to the left:

x^2+20x-(-2x^2+10x+3000)=0

We get rid of parentheses

x^2+2x^2-10x+20x-3000=0

We add all the numbers together, and all the variables

3x^2+10x-3000=0

a = 3; b = 10; c = -3000;
Δ = b2-4ac
Δ = 102-4·3·(-3000)
Δ = 36100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36100}=190$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-190}{2*3}=\frac{-200}{6}
=-33+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+190}{2*3}=\frac{180}{6}
=30
$