1/7x-11=1/4x-14

Solution for 1/7x-11=1/4x-14 equation:

1/7x-11=1/4x-14

We move all terms to the left:

1/7x-11-(1/4x-14)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 4x-14)!=0

x∈R


We get rid of parentheses

1/7x-1/4x+14-11=0

We calculate fractions


4x/28x^2+(-7x)/28x^2+14-11=0

We add all the numbers together, and all the variables

4x/28x^2+(-7x)/28x^2+3=0

We multiply all the terms by the denominator


4x+(-7x)+3*28x^2=0

Wy multiply elements

84x^2+4x+(-7x)=0

We get rid of parentheses

84x^2+4x-7x=0

We add all the numbers together, and all the variables

84x^2-3x=0

a = 84; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·84·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*84}=\frac{0}{168}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*84}=\frac{6}{168}
=1/28
$