-(2)/(3)x-(3)/(4)x=(5)/(6)

Solution for -(2)/(3)x-(3)/(4)x=(5)/(6) equation:

-(2)/(3)x-(3)/(4)x=(5)/(6)

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

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

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

We get rid of parentheses

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

We calculate fractions


(-240x^2)/432x^2+(-288x)/432x^2+(-324x)/432x^2=0

We multiply all the terms by the denominator


(-240x^2)+(-288x)+(-324x)=0

We get rid of parentheses

-240x^2-288x-324x=0

We add all the numbers together, and all the variables

-240x^2-612x=0

a = -240; b = -612; c = 0;
Δ = b2-4ac
Δ = -6122-4·(-240)·0
Δ = 374544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{374544}=612$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-612)-612}{2*-240}=\frac{0}{-480}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-612)+612}{2*-240}=\frac{1224}{-480}
=-2+11/20
$