5/6x+2/3-3/4x=21/2

Solution for 5/6x+2/3-3/4x=21/2 equation:

5/6x+2/3-3/4x=21/2

We move all terms to the left:

5/6x+2/3-3/4x-(21/2)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x-3/4x+2/3-(+21/2)=0

We get rid of parentheses

5/6x-3/4x+2/3-21/2=0

We calculate fractions


(-6048x^2)/432x^2+384x^2/432x^2+360x/432x^2+(-324x)/432x^2=0

We multiply all the terms by the denominator


(-6048x^2)+384x^2+360x+(-324x)=0

We add all the numbers together, and all the variables

384x^2+(-6048x^2)+360x+(-324x)=0

We get rid of parentheses

384x^2-6048x^2+360x-324x=0

We add all the numbers together, and all the variables

-5664x^2+36x=0

a = -5664; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-5664)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-5664}=\frac{-72}{-11328}
=3/472
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-5664}=\frac{0}{-11328}
=0
$