2x+4/5x=8

Solution for 2x+4/5x=8 equation:

2x+4/5x=8

We move all terms to the left:

2x+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


2x*5x-8*5x+4=0

Wy multiply elements

10x^2-40x+4=0

a = 10; b = -40; c = +4;
Δ = b2-4ac
Δ = -402-4·10·4
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-12\sqrt{10}}{2*10}=\frac{40-12\sqrt{10}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+12\sqrt{10}}{2*10}=\frac{40+12\sqrt{10}}{20}
$