3/5x+x=4

Solution for 3/5x+x=4 equation:

3/5x+x=4

We move all terms to the left:

3/5x+x-(4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/5x-4=0

We multiply all the terms by the denominator


x*5x-4*5x+3=0

Wy multiply elements

5x^2-20x+3=0

a = 5; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·5·3
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{85}}{2*5}=\frac{20-2\sqrt{85}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{85}}{2*5}=\frac{20+2\sqrt{85}}{10}
$