8y2-12y+4=y+10

Solution for 8y2-12y+4=y+10 equation:

8y^2-12y+4=y+10

We move all terms to the left:

8y^2-12y+4-(y+10)=0

We get rid of parentheses

8y^2-12y-y-10+4=0

We add all the numbers together, and all the variables

8y^2-13y-6=0

a = 8; b = -13; c = -6;
Δ = b2-4ac
Δ = -132-4·8·(-6)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-19}{2*8}=\frac{-6}{16}
=-3/8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+19}{2*8}=\frac{32}{16}
=2
$