6y^2+17y=39

Solution for 6y^2+17y=39 equation:

6y^2+17y=39

We move all terms to the left:

6y^2+17y-(39)=0

a = 6; b = 17; c = -39;
Δ = b2-4ac
Δ = 172-4·6·(-39)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-35}{2*6}=\frac{-52}{12}
=-4+1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+35}{2*6}=\frac{18}{12}
=1+1/2
$