-1/2x+10+1=3/x+5

Solution for -1/2x+10+1=3/x+5 equation:

-1/2x+10+1=3/x+5

We move all terms to the left:

-1/2x+10+1-(3/x+5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

-1/2x-(3/x+5)+11=0

We get rid of parentheses

-1/2x-3/x-5+11=0

We calculate fractions


(-x)/2x^2+(-6x)/2x^2-5+11=0

We add all the numbers together, and all the variables

(-1x)/2x^2+(-6x)/2x^2-5+11=0

We add all the numbers together, and all the variables

(-1x)/2x^2+(-6x)/2x^2+6=0

We multiply all the terms by the denominator


(-1x)+(-6x)+6*2x^2=0

Wy multiply elements

12x^2+(-1x)+(-6x)=0

We get rid of parentheses

12x^2-1x-6x=0

We add all the numbers together, and all the variables

12x^2-7x=0

a = 12; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·12·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*12}=\frac{14}{24}
=7/12
$