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96=-31a(7+3a)
We move all terms to the left:
96-(-31a(7+3a))=0
We add all the numbers together, and all the variables
-(-31a(3a+7))+96=0
We calculate terms in parentheses: -(-31a(3a+7)), so:We get rid of parentheses
-31a(3a+7)
We multiply parentheses
-93a^2-217a
Back to the equation:
-(-93a^2-217a)
93a^2+217a+96=0
a = 93; b = 217; c = +96;
Δ = b2-4ac
Δ = 2172-4·93·96
Δ = 11377
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{-(217)-\sqrt{11377}}{2*93}=\frac{-217-\sqrt{11377}}{186} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(217)+\sqrt{11377}}{2*93}=\frac{-217+\sqrt{11377}}{186} $
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