5/x-2+3x/4x-8=0

Solution for 5/x-2+3x/4x-8=0 equation:

5/x-2+3x/4x-8=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5/x+3x/4x-10=0

We calculate fractions


3x^2/4x^2+20x/4x^2-10=0

We multiply all the terms by the denominator


3x^2+20x-10*4x^2=0

Wy multiply elements

3x^2-40x^2+20x=0

We add all the numbers together, and all the variables

-37x^2+20x=0

a = -37; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-37)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-37}=\frac{-40}{-74}
=20/37
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-37}=\frac{0}{-74}
=0
$