8x-(5*9x-4)8x=-17

Solution for 8x-(5*9x-4)8x=-17 equation:

8x-(5*9x-4)8x=-17

We move all terms to the left:

8x-(5*9x-4)8x-(-17)=0

We add all the numbers together, and all the variables

8x-(5*9x-4)8x+17=0

We multiply parentheses

-360x^2+8x+32x+17=0

We add all the numbers together, and all the variables

-360x^2+40x+17=0

a = -360; b = 40; c = +17;
Δ = b2-4ac
Δ = 402-4·(-360)·17
Δ = 26080
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:

$\sqrt{\Delta}=\sqrt{26080}=\sqrt{16*1630}=\sqrt{16}*\sqrt{1630}=4\sqrt{1630}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{1630}}{2*-360}=\frac{-40-4\sqrt{1630}}{-720}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{1630}}{2*-360}=\frac{-40+4\sqrt{1630}}{-720}
$