8/x+4=5/7x

Solution for 8/x+4=5/7x equation:

8/x+4=5/7x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


56x/7x^2+(-5x)/7x^2+4=0

We multiply all the terms by the denominator


56x+(-5x)+4*7x^2=0

Wy multiply elements

28x^2+56x+(-5x)=0

We get rid of parentheses

28x^2+56x-5x=0

We add all the numbers together, and all the variables

28x^2+51x=0

a = 28; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·28·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*28}=\frac{-102}{56}
=-1+23/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*28}=\frac{0}{56}
=0
$