5/x-4+6/5x-20=10

Solution for 5/x-4+6/5x-20=10 equation:

5/x-4+6/5x-20=10

We move all terms to the left:

5/x-4+6/5x-20-(10)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

5/x+6/5x-34=0

We calculate fractions


25x/5x^2+6x/5x^2-34=0

We multiply all the terms by the denominator


25x+6x-34*5x^2=0

We add all the numbers together, and all the variables

31x-34*5x^2=0

Wy multiply elements

-170x^2+31x=0

a = -170; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-170)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-170}=\frac{-62}{-340}
=31/170
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-170}=\frac{0}{-340}
=0
$