4x+1/5x=8

Solution for 4x+1/5x=8 equation:

4x+1/5x=8

We move all terms to the left:

4x+1/5x-(8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


4x*5x-8*5x+1=0

Wy multiply elements

20x^2-40x+1=0

a = 20; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·20·1
Δ = 1520
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:

$\sqrt{\Delta}=\sqrt{1520}=\sqrt{16*95}=\sqrt{16}*\sqrt{95}=4\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{95}}{2*20}=\frac{40-4\sqrt{95}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{95}}{2*20}=\frac{40+4\sqrt{95}}{40}
$