5/6x+2/3x=11/2

Solution for 5/6x+2/3x=11/2 equation:

5/6x+2/3x=11/2

We move all terms to the left:

5/6x+2/3x-(11/2)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x+2/3x-(+11/2)=0

We get rid of parentheses

5/6x+2/3x-11/2=0

We calculate fractions


(-594x^2)/72x^2+60x/72x^2+48x/72x^2=0

We multiply all the terms by the denominator


(-594x^2)+60x+48x=0

We add all the numbers together, and all the variables

(-594x^2)+108x=0

We get rid of parentheses

-594x^2+108x=0

a = -594; b = 108; c = 0;
Δ = b2-4ac
Δ = 1082-4·(-594)·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108}{2*-594}=\frac{-216}{-1188}
=2/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108}{2*-594}=\frac{0}{-1188}
=0
$