8x((3)/(5))=512

Solution for 8x((3)/(5))=512 equation:

8x((3)/(5))=512

We move all terms to the left:

8x((3)/(5))-(512)=0

We add all the numbers together, and all the variables

8x(+3/5)-512=0

We multiply parentheses

24x^2-512=0

a = 24; b = 0; c = -512;
Δ = b2-4ac
Δ = 02-4·24·(-512)
Δ = 49152
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:

$\sqrt{\Delta}=\sqrt{49152}=\sqrt{16384*3}=\sqrt{16384}*\sqrt{3}=128\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-128\sqrt{3}}{2*24}=\frac{0-128\sqrt{3}}{48}
=-\frac{128\sqrt{3}}{48}
=-\frac{8\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+128\sqrt{3}}{2*24}=\frac{0+128\sqrt{3}}{48}
=\frac{128\sqrt{3}}{48}
=\frac{8\sqrt{3}}{3}
$