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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} $
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