4/3x+5/6x=13

Solution for 4/3x+5/6x=13 equation:

4/3x+5/6x=13

We move all terms to the left:

4/3x+5/6x-(13)=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 calculate fractions


24x/18x^2+15x/18x^2-13=0

We multiply all the terms by the denominator


24x+15x-13*18x^2=0

We add all the numbers together, and all the variables

39x-13*18x^2=0

Wy multiply elements

-234x^2+39x=0

a = -234; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·(-234)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*-234}=\frac{-78}{-468}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*-234}=\frac{0}{-468}
=0
$