X^2-x=6x-6

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

X^2-X=6X-6

We move all terms to the left:

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

We add all the numbers together, and all the variables

X^2-1X-(6X-6)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

X^2-7X+6=0

a = 1; b = -7; c = +6;
Δ = b2-4ac
Δ = -72-4·1·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*1}=\frac{2}{2}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*1}=\frac{12}{2}
=6
$