96=-31a(7+3a)

Solution for 96=-31a(7+3a) equation:

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:

-31a(3a+7)

We multiply parentheses

-93a^2-217a

Back to the equation:

-(-93a^2-217a)


We get rid of parentheses

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}
$