3+8y^2=10y

Solution for 3+8y^2=10y equation:

3+8y^2=10y

We move all terms to the left:

3+8y^2-(10y)=0

a = 8; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·8·3
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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