5/3x+4/6x=36/9

Solution for 5/3x+4/6x=36/9 equation:

5/3x+4/6x=36/9

We move all terms to the left:

5/3x+4/6x-(36/9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


30x/18x^2+12x/18x^2-4=0

We multiply all the terms by the denominator


30x+12x-4*18x^2=0

We add all the numbers together, and all the variables

42x-4*18x^2=0

Wy multiply elements

-72x^2+42x=0

a = -72; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·(-72)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*-72}=\frac{-84}{-144}
=7/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*-72}=\frac{0}{-144}
=0
$