2y^2+12y=7

Solution for 2y^2+12y=7 equation:

2y^2+12y=7

We move all terms to the left:

2y^2+12y-(7)=0

a = 2; b = 12; c = -7;
Δ = b2-4ac
Δ = 122-4·2·(-7)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-10\sqrt{2}}{2*2}=\frac{-12-10\sqrt{2}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+10\sqrt{2}}{2*2}=\frac{-12+10\sqrt{2}}{4}
$