(4y^2-9y)-(-5y^2+8y-8)=y

Solution for (4y^2-9y)-(-5y^2+8y-8)=y equation:

(4y^2-9y)-(-5y^2+8y-8)=y

We move all terms to the left:

(4y^2-9y)-(-5y^2+8y-8)-(y)=0

We add all the numbers together, and all the variables

-(-5y^2+8y-8)-1y+(4y^2-9y)=0

We get rid of parentheses

5y^2+4y^2-8y-1y-9y+8=0

We add all the numbers together, and all the variables

9y^2-18y+8=0

a = 9; b = -18; c = +8;
Δ = b2-4ac
Δ = -182-4·9·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6}{2*9}=\frac{12}{18}
=2/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6}{2*9}=\frac{24}{18}
=1+1/3
$