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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


204x^2/72x^2+96x/72x^2+(-108x)/72x^2-1=0

We multiply all the terms by the denominator


204x^2+96x+(-108x)-1*72x^2=0

Wy multiply elements

204x^2-72x^2+96x+(-108x)=0

We get rid of parentheses

204x^2-72x^2+96x-108x=0

We add all the numbers together, and all the variables

132x^2-12x=0

a = 132; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·132·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*132}=\frac{0}{264}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*132}=\frac{24}{264}
=1/11
$