y2+12y=37

Solution for y2+12y=37 equation:

y2+12y=37

We move all terms to the left:

y2+12y-(37)=0

We add all the numbers together, and all the variables

y^2+12y-37=0

a = 1; b = 12; c = -37;
Δ = b2-4ac
Δ = 122-4·1·(-37)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{73}}{2*1}=\frac{-12-2\sqrt{73}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{73}}{2*1}=\frac{-12+2\sqrt{73}}{2}
$