1/6x+14=3/4x

Solution for 1/6x+14=3/4x equation:

1/6x+14=3/4x

We move all terms to the left:

1/6x+14-(3/4x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/6x-(+3/4x)+14=0

We get rid of parentheses

1/6x-3/4x+14=0

We calculate fractions


4x/24x^2+(-18x)/24x^2+14=0

We multiply all the terms by the denominator


4x+(-18x)+14*24x^2=0

Wy multiply elements

336x^2+4x+(-18x)=0

We get rid of parentheses

336x^2+4x-18x=0

We add all the numbers together, and all the variables

336x^2-14x=0

a = 336; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·336·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*336}=\frac{0}{672}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*336}=\frac{28}{672}
=1/24
$