8-3y=7y2-5y

Solution for 8-3y=7y2-5y equation:

8-3y=7y^2-5y

We move all terms to the left:

8-3y-(7y^2-5y)=0

We get rid of parentheses

-7y^2-3y+5y+8=0

We add all the numbers together, and all the variables

-7y^2+2y+8=0

a = -7; b = 2; c = +8;
Δ = b2-4ac
Δ = 22-4·(-7)·8
Δ = 228
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{57}}{2*-7}=\frac{-2-2\sqrt{57}}{-14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{57}}{2*-7}=\frac{-2+2\sqrt{57}}{-14}
$