6y+(2y^2)=172

Solution for 6y+(2y^2)=172 equation:

6y+(2y^2)=172

We move all terms to the left:

6y+(2y^2)-(172)=0

determiningTheFunctionDomain
2y^2+6y-172=0

a = 2; b = 6; c = -172;
Δ = b2-4ac
Δ = 62-4·2·(-172)
Δ = 1412
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:

$\sqrt{\Delta}=\sqrt{1412}=\sqrt{4*353}=\sqrt{4}*\sqrt{353}=2\sqrt{353}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{353}}{2*2}=\frac{-6-2\sqrt{353}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{353}}{2*2}=\frac{-6+2\sqrt{353}}{4}
$