x(8x-9)=90

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

x(8x-9)=90

We move all terms to the left:

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

We multiply parentheses

8x^2-9x-90=0

a = 8; b = -9; c = -90;
Δ = b2-4ac
Δ = -92-4·8·(-90)
Δ = 2961
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:

$\sqrt{\Delta}=\sqrt{2961}=\sqrt{9*329}=\sqrt{9}*\sqrt{329}=3\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{329}}{2*8}=\frac{9-3\sqrt{329}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{329}}{2*8}=\frac{9+3\sqrt{329}}{16}
$