X^2-6x=-x^2+20

Solution for X^2-6x=-x^2+20 equation:

X^2-6X=-X^2+20

We move all terms to the left:

X^2-6X-(-X^2+20)=0

We get rid of parentheses

X^2+X^2-6X-20=0

We add all the numbers together, and all the variables

2X^2-6X-20=0

a = 2; b = -6; c = -20;
Δ = b2-4ac
Δ = -62-4·2·(-20)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-14}{2*2}=\frac{-8}{4}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+14}{2*2}=\frac{20}{4}
=5
$