8y^2=8y-9-35y

Solution for 8y^2=8y-9-35y equation:

8y^2=8y-9-35y

We move all terms to the left:

8y^2-(8y-9-35y)=0

We add all the numbers together, and all the variables

8y^2-(-27y-9)=0

We get rid of parentheses

8y^2+27y+9=0

a = 8; b = 27; c = +9;
Δ = b2-4ac
Δ = 272-4·8·9
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-21}{2*8}=\frac{-48}{16}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+21}{2*8}=\frac{-6}{16}
=-3/8
$