12.17=4y+3y^2

Solution for 12.17=4y+3y^2 equation:

12.17=4y+3y^2

We move all terms to the left:

12.17-(4y+3y^2)=0

We get rid of parentheses

-3y^2-4y+12.17=0

a = -3; b = -4; c = +12.17;
Δ = b2-4ac
Δ = -42-4·(-3)·12.17
Δ = 162.04
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{-(-4)-\sqrt{162.04}}{2*-3}=\frac{4-\sqrt{162.04}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+\sqrt{162.04}}{2*-3}=\frac{4+\sqrt{162.04}}{-6}
$