8y-3y2=2

Solution for 8y-3y2=2 equation:

8y-3y^2=2

We move all terms to the left:

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

a = -3; b = 8; c = -2;
Δ = b2-4ac
Δ = 82-4·(-3)·(-2)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{10}}{2*-3}=\frac{-8-2\sqrt{10}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{10}}{2*-3}=\frac{-8+2\sqrt{10}}{-6}
$