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a^2+5a=84
We move all terms to the left:
a^2+5a-(84)=0
a = 1; b = 5; c = -84;
Δ = b2-4ac
Δ = 52-4·1·(-84)
Δ = 361
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{361}=19$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*1}=\frac{-24}{2} =-12 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*1}=\frac{14}{2} =7 $
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