x-4/5x=8

Solution for x-4/5x=8 equation:

x-4/5x=8

We move all terms to the left:

x-4/5x-(8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


x*5x-8*5x-4=0

Wy multiply elements

5x^2-40x-4=0

a = 5; b = -40; c = -4;
Δ = b2-4ac
Δ = -402-4·5·(-4)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{105}}{2*5}=\frac{40-4\sqrt{105}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{105}}{2*5}=\frac{40+4\sqrt{105}}{10}
$