3/x-1/4x+14=3

Solution for 3/x-1/4x+14=3 equation:

3/x-1/4x+14=3

We move all terms to the left:

3/x-1/4x+14-(3)=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

3/x-1/4x+11=0

We calculate fractions


12x/4x^2+(-x)/4x^2+11=0

We add all the numbers together, and all the variables

12x/4x^2+(-1x)/4x^2+11=0

We multiply all the terms by the denominator


12x+(-1x)+11*4x^2=0

Wy multiply elements

44x^2+12x+(-1x)=0

We get rid of parentheses

44x^2+12x-1x=0

We add all the numbers together, and all the variables

44x^2+11x=0

a = 44; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·44·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*44}=\frac{-22}{88}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*44}=\frac{0}{88}
=0
$