1/3x+21/6x=1

Solution for 1/3x+21/6x=1 equation:

1/3x+21/6x=1

We move all terms to the left:

1/3x+21/6x-(1)=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


6x/18x^2+63x/18x^2-1=0

We multiply all the terms by the denominator


6x+63x-1*18x^2=0

We add all the numbers together, and all the variables

69x-1*18x^2=0

Wy multiply elements

-18x^2+69x=0

a = -18; b = 69; c = 0;
Δ = b2-4ac
Δ = 692-4·(-18)·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-69}{2*-18}=\frac{-138}{-36}
=3+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+69}{2*-18}=\frac{0}{-36}
=0
$