4/7x=2/x-5

Solution for 4/7x=2/x-5 equation:

4/7x=2/x-5

We move all terms to the left:

4/7x-(2/x-5)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: x-5)!=0

x∈R


We get rid of parentheses

4/7x-2/x+5=0

We calculate fractions


4x/7x^2+(-14x)/7x^2+5=0

We multiply all the terms by the denominator


4x+(-14x)+5*7x^2=0

Wy multiply elements

35x^2+4x+(-14x)=0

We get rid of parentheses

35x^2+4x-14x=0

We add all the numbers together, and all the variables

35x^2-10x=0

a = 35; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·35·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*35}=\frac{0}{70}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*35}=\frac{20}{70}
=2/7
$