10/x=-2/4x+5

Solution for 10/x=-2/4x+5 equation:

10/x=-2/4x+5

We move all terms to the left:

10/x-(-2/4x+5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x+5)!=0

x∈R


We get rid of parentheses

10/x+2/4x-5=0

We calculate fractions


40x/4x^2+2x/4x^2-5=0

We multiply all the terms by the denominator


40x+2x-5*4x^2=0

We add all the numbers together, and all the variables

42x-5*4x^2=0

Wy multiply elements

-20x^2+42x=0

a = -20; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·(-20)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*-20}=\frac{-84}{-40}
=2+1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*-20}=\frac{0}{-40}
=0
$