x2-x-6=-x2+x

Solution for x2-x-6=-x2+x equation:

x2-x-6=-x2+x

We move all terms to the left:

x2-x-6-(-x2+x)=0

We add all the numbers together, and all the variables

-(-1x^2+x)+x2-x-6=0

We add all the numbers together, and all the variables

x^2-(-1x^2+x)-1x-6=0

We get rid of parentheses

x^2+1x^2-x-1x-6=0

We add all the numbers together, and all the variables

2x^2-2x-6=0

a = 2; b = -2; c = -6;
Δ = b2-4ac
Δ = -22-4·2·(-6)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{13}}{2*2}=\frac{2-2\sqrt{13}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{13}}{2*2}=\frac{2+2\sqrt{13}}{4}
$