3/x=11+14x

Solution for 3/x=11+14x equation:

3/x=11+14x

We move all terms to the left:

3/x-(11+14x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3/x-(14x+11)=0

We get rid of parentheses

3/x-14x-11=0

We multiply all the terms by the denominator


-14x*x-11*x+3=0

We add all the numbers together, and all the variables

-11x-14x*x+3=0

Wy multiply elements

-14x^2-11x+3=0

a = -14; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·(-14)·3
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-17}{2*-14}=\frac{-6}{-28}
=3/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+17}{2*-14}=\frac{28}{-28}
=-1
$