84=2y^2+6y

Solution for 84=2y^2+6y equation:

84=2y^2+6y

We move all terms to the left:

84-(2y^2+6y)=0

We get rid of parentheses

-2y^2-6y+84=0

a = -2; b = -6; c = +84;
Δ = b2-4ac
Δ = -62-4·(-2)·84
Δ = 708
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:

$\sqrt{\Delta}=\sqrt{708}=\sqrt{4*177}=\sqrt{4}*\sqrt{177}=2\sqrt{177}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{177}}{2*-2}=\frac{6-2\sqrt{177}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{177}}{2*-2}=\frac{6+2\sqrt{177}}{-4}
$