2y-3=-8y^2

Solution for 2y-3=-8y^2 equation:

2y-3=-8y^2

We move all terms to the left:

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

We get rid of parentheses

8y^2+2y-3=0

a = 8; b = 2; c = -3;
Δ = b2-4ac
Δ = 22-4·8·(-3)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*8}=\frac{-12}{16}
=-3/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*8}=\frac{8}{16}
=1/2
$