(6x^2-2x+2)-(5x^2+2x-2)=1

Solution for (6x^2-2x+2)-(5x^2+2x-2)=1 equation:

(6x^2-2x+2)-(5x^2+2x-2)=1

We move all terms to the left:

(6x^2-2x+2)-(5x^2+2x-2)-(1)=0

We get rid of parentheses

6x^2-5x^2-2x-2x+2+2-1=0

We add all the numbers together, and all the variables

x^2-4x+3=0

a = 1; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·1·3
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2}{2*1}=\frac{6}{2}
=3
$