5=8i(9i-9)

Solution for 5=8i(9i-9) equation:

5=8i(9i-9)

We move all terms to the left:

5-(8i(9i-9))=0


We calculate terms in parentheses: -(8i(9i-9)), so:

8i(9i-9)

We multiply parentheses

72i^2-72i

Back to the equation:

-(72i^2-72i)


We get rid of parentheses

-72i^2+72i+5=0

a = -72; b = 72; c = +5;
Δ = b2-4ac
Δ = 722-4·(-72)·5
Δ = 6624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6624}=\sqrt{144*46}=\sqrt{144}*\sqrt{46}=12\sqrt{46}$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12\sqrt{46}}{2*-72}=\frac{-72-12\sqrt{46}}{-144}
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12\sqrt{46}}{2*-72}=\frac{-72+12\sqrt{46}}{-144}
$