x(9x+8)=4

Solution for x(9x+8)=4 equation:

x(9x+8)=4

We move all terms to the left:

x(9x+8)-(4)=0

We multiply parentheses

9x^2+8x-4=0

a = 9; b = 8; c = -4;
Δ = b2-4ac
Δ = 82-4·9·(-4)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{13}}{2*9}=\frac{-8-4\sqrt{13}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{13}}{2*9}=\frac{-8+4\sqrt{13}}{18}
$