x/3x-7x+22=2

Solution for x/3x-7x+22=2 equation:

x/3x-7x+22=2

We move all terms to the left:

x/3x-7x+22-(2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-7x+x/3x+20=0

We multiply all the terms by the denominator


-7x*3x+x+20*3x=0

We add all the numbers together, and all the variables

x-7x*3x+20*3x=0

Wy multiply elements

-21x^2+x+60x=0

We add all the numbers together, and all the variables

-21x^2+61x=0

a = -21; b = 61; c = 0;
Δ = b2-4ac
Δ = 612-4·(-21)·0
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-61}{2*-21}=\frac{-122}{-42}
=2+19/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+61}{2*-21}=\frac{0}{-42}
=0
$