7y^2=8-5y

Solution for 7y^2=8-5y equation:

7y^2=8-5y

We move all terms to the left:

7y^2-(8-5y)=0

We add all the numbers together, and all the variables

7y^2-(-5y+8)=0

We get rid of parentheses

7y^2+5y-8=0

a = 7; b = 5; c = -8;
Δ = b2-4ac
Δ = 52-4·7·(-8)
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{249}}{2*7}=\frac{-5-\sqrt{249}}{14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{249}}{2*7}=\frac{-5+\sqrt{249}}{14}
$