5/12x-7=3/4x+14

Solution for 5/12x-7=3/4x+14 equation:

5/12x-7=3/4x+14

We move all terms to the left:

5/12x-7-(3/4x+14)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



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

x∈R


We get rid of parentheses

5/12x-3/4x-14-7=0

We calculate fractions


20x/48x^2+(-36x)/48x^2-14-7=0

We add all the numbers together, and all the variables

20x/48x^2+(-36x)/48x^2-21=0

We multiply all the terms by the denominator


20x+(-36x)-21*48x^2=0

Wy multiply elements

-1008x^2+20x+(-36x)=0

We get rid of parentheses

-1008x^2+20x-36x=0

We add all the numbers together, and all the variables

-1008x^2-16x=0

a = -1008; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-1008)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-1008}=\frac{0}{-2016}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-1008}=\frac{32}{-2016}
=-1/63
$