2/3x+17/12=1/4x+1

Solution for 2/3x+17/12=1/4x+1 equation:

2/3x+17/12=1/4x+1

We move all terms to the left:

2/3x+17/12-(1/4x+1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

2/3x-1/4x-1+17/12=0

We calculate fractions


816x^2/144x^2+96x/144x^2+(-36x)/144x^2-1=0

We multiply all the terms by the denominator


816x^2+96x+(-36x)-1*144x^2=0

Wy multiply elements

816x^2-144x^2+96x+(-36x)=0

We get rid of parentheses

816x^2-144x^2+96x-36x=0

We add all the numbers together, and all the variables

672x^2+60x=0

a = 672; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·672·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*672}=\frac{-120}{1344}
=-5/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*672}=\frac{0}{1344}
=0
$