96=b(2b-8)

Solution for 96=b(2b-8) equation:

96=b(2b-8)

We move all terms to the left:

96-(b(2b-8))=0


We calculate terms in parentheses: -(b(2b-8)), so:

b(2b-8)

We multiply parentheses

2b^2-8b

Back to the equation:

-(2b^2-8b)


We get rid of parentheses

-2b^2+8b+96=0

a = -2; b = 8; c = +96;
Δ = b2-4ac
Δ = 82-4·(-2)·96
Δ = 832
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{13}}{2*-2}=\frac{-8-8\sqrt{13}}{-4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{13}}{2*-2}=\frac{-8+8\sqrt{13}}{-4}
$