3/8x-1=5/x-4

Solution for 3/8x-1=5/x-4 equation:

3/8x-1=5/x-4

We move all terms to the left:

3/8x-1-(5/x-4)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: x-4)!=0

x∈R


We get rid of parentheses

3/8x-5/x+4-1=0

We calculate fractions


3x/8x^2+(-40x)/8x^2+4-1=0

We add all the numbers together, and all the variables

3x/8x^2+(-40x)/8x^2+3=0

We multiply all the terms by the denominator


3x+(-40x)+3*8x^2=0

Wy multiply elements

24x^2+3x+(-40x)=0

We get rid of parentheses

24x^2+3x-40x=0

We add all the numbers together, and all the variables

24x^2-37x=0

a = 24; b = -37; c = 0;
Δ = b2-4ac
Δ = -372-4·24·0
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-37}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+37}{2*24}=\frac{74}{48}
=1+13/24
$