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y^2+7y+8y=-6
We move all terms to the left:
y^2+7y+8y-(-6)=0
We add all the numbers together, and all the variables
y^2+15y+6=0
a = 1; b = 15; c = +6;
Δ = b2-4ac
Δ = 152-4·1·6
Δ = 201
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{201}}{2*1}=\frac{-15-\sqrt{201}}{2} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{201}}{2*1}=\frac{-15+\sqrt{201}}{2} $
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