4/5x+7=5/x-1

Solution for 4/5x+7=5/x-1 equation:

4/5x+7=5/x-1

We move all terms to the left:

4/5x+7-(5/x-1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: x-1)!=0

x∈R


We get rid of parentheses

4/5x-5/x+1+7=0

We calculate fractions


4x/5x^2+(-25x)/5x^2+1+7=0

We add all the numbers together, and all the variables

4x/5x^2+(-25x)/5x^2+8=0

We multiply all the terms by the denominator


4x+(-25x)+8*5x^2=0

Wy multiply elements

40x^2+4x+(-25x)=0

We get rid of parentheses

40x^2+4x-25x=0

We add all the numbers together, and all the variables

40x^2-21x=0

a = 40; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·40·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*40}=\frac{0}{80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*40}=\frac{42}{80}
=21/40
$