8x(x^-9)=90

Solution for 8x(x^-9)=90 equation:

8x(x^-9)=90

We move all terms to the left:

8x(x^-9)-(90)=0

We multiply parentheses

8x^2-72x-90=0

a = 8; b = -72; c = -90;
Δ = b2-4ac
Δ = -722-4·8·(-90)
Δ = 8064
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8064}=\sqrt{576*14}=\sqrt{576}*\sqrt{14}=24\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-24\sqrt{14}}{2*8}=\frac{72-24\sqrt{14}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+24\sqrt{14}}{2*8}=\frac{72+24\sqrt{14}}{16}
$