X^2+2x=5x+20

Solution for X^2+2x=5x+20 equation:

X^2+2X=5X+20

We move all terms to the left:

X^2+2X-(5X+20)=0

We get rid of parentheses

X^2+2X-5X-20=0

We add all the numbers together, and all the variables

X^2-3X-20=0

a = 1; b = -3; c = -20;
Δ = b2-4ac
Δ = -32-4·1·(-20)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{89}}{2*1}=\frac{3-\sqrt{89}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{89}}{2*1}=\frac{3+\sqrt{89}}{2}
$