8x(3x-5)=20

Solution for 8x(3x-5)=20 equation:

8x(3x-5)=20

We move all terms to the left:

8x(3x-5)-(20)=0

We multiply parentheses

24x^2-40x-20=0

a = 24; b = -40; c = -20;
Δ = b2-4ac
Δ = -402-4·24·(-20)
Δ = 3520
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:

$\sqrt{\Delta}=\sqrt{3520}=\sqrt{64*55}=\sqrt{64}*\sqrt{55}=8\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{55}}{2*24}=\frac{40-8\sqrt{55}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{55}}{2*24}=\frac{40+8\sqrt{55}}{48}
$