8/5x-8=2x

Solution for 8/5x-8=2x equation:

8/5x-8=2x

We move all terms to the left:

8/5x-8-(2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+8/5x-8=0

We multiply all the terms by the denominator


-2x*5x-8*5x+8=0

Wy multiply elements

-10x^2-40x+8=0

a = -10; b = -40; c = +8;
Δ = b2-4ac
Δ = -402-4·(-10)·8
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{30}}{2*-10}=\frac{40-8\sqrt{30}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{30}}{2*-10}=\frac{40+8\sqrt{30}}{-20}
$