8x(3x-5)=5

Solution for 8x(3x-5)=5 equation:

8x(3x-5)=5

We move all terms to the left:

8x(3x-5)-(5)=0

We multiply parentheses

24x^2-40x-5=0

a = 24; b = -40; c = -5;
Δ = b2-4ac
Δ = -402-4·24·(-5)
Δ = 2080
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:

$\sqrt{\Delta}=\sqrt{2080}=\sqrt{16*130}=\sqrt{16}*\sqrt{130}=4\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{130}}{2*24}=\frac{40-4\sqrt{130}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{130}}{2*24}=\frac{40+4\sqrt{130}}{48}
$