8x(x-2)-5=0

Solution for 8x(x-2)-5=0 equation:

8x(x-2)-5=0

We multiply parentheses

8x^2-16x-5=0

a = 8; b = -16; c = -5;
Δ = b2-4ac
Δ = -162-4·8·(-5)
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{26}}{2*8}=\frac{16-4\sqrt{26}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{26}}{2*8}=\frac{16+4\sqrt{26}}{16}
$