10x-x^2=2x+x^2

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

10x-x^2=2x+x^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x^2-(2x+x^2)+10x=0

We get rid of parentheses

-1x^2-x^2-2x+10x=0

We add all the numbers together, and all the variables

-2x^2+8x=0

a = -2; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-2)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-2}=\frac{0}{-4}
=0
$