-2/x+1/4x=7/x+10

Solution for -2/x+1/4x=7/x+10 equation:

-2/x+1/4x=7/x+10

We move all terms to the left:

-2/x+1/4x-(7/x+10)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x+10)!=0

x∈R


We get rid of parentheses

-2/x+1/4x-7/x-10=0

We calculate fractions


(-28x-2)/4x^2+x/4x^2-10=0

We multiply all the terms by the denominator


(-28x-2)+x-10*4x^2=0

We add all the numbers together, and all the variables

x+(-28x-2)-10*4x^2=0

Wy multiply elements

-40x^2+x+(-28x-2)=0

We get rid of parentheses

-40x^2+x-28x-2=0

We add all the numbers together, and all the variables

-40x^2-27x-2=0

a = -40; b = -27; c = -2;
Δ = b2-4ac
Δ = -272-4·(-40)·(-2)
Δ = 409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{409}}{2*-40}=\frac{27-\sqrt{409}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{409}}{2*-40}=\frac{27+\sqrt{409}}{-80}
$