y^2-y-6=2y^2-8y

Solution for y^2-y-6=2y^2-8y equation:

y^2-y-6=2y^2-8y

We move all terms to the left:

y^2-y-6-(2y^2-8y)=0

We add all the numbers together, and all the variables

y^2-1y-(2y^2-8y)-6=0

We get rid of parentheses

y^2-2y^2-1y+8y-6=0

We add all the numbers together, and all the variables

-1y^2+7y-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:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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