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a(a+7)-7=9
We move all terms to the left:
a(a+7)-7-(9)=0
We add all the numbers together, and all the variables
a(a+7)-16=0
We multiply parentheses
a^2+7a-16=0
a = 1; b = 7; c = -16;
Δ = b2-4ac
Δ = 72-4·1·(-16)
Δ = 113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{113}}{2*1}=\frac{-7-\sqrt{113}}{2} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{113}}{2*1}=\frac{-7+\sqrt{113}}{2} $
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