8/3x+5/6x=14

Solution for 8/3x+5/6x=14 equation:

8/3x+5/6x=14

We move all terms to the left:

8/3x+5/6x-(14)=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


48x/18x^2+15x/18x^2-14=0

We multiply all the terms by the denominator


48x+15x-14*18x^2=0

We add all the numbers together, and all the variables

63x-14*18x^2=0

Wy multiply elements

-252x^2+63x=0

a = -252; b = 63; c = 0;
Δ = b2-4ac
Δ = 632-4·(-252)·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-63}{2*-252}=\frac{-126}{-504}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*-252}=\frac{0}{-504}
=0
$