17y=-7-6y^2

Solution for 17y=-7-6y^2 equation:

17y=-7-6y^2

We move all terms to the left:

17y-(-7-6y^2)=0

We get rid of parentheses

6y^2+17y+7=0

a = 6; b = 17; c = +7;
Δ = b2-4ac
Δ = 172-4·6·7
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-11}{2*6}=\frac{-28}{12}
=-2+1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+11}{2*6}=\frac{-6}{12}
=-1/2
$