1/7*x+1/3*x=20

Solution for 1/7*x+1/3*x=20 equation:

1/7x+1/3x=20

We move all terms to the left:

1/7x+1/3x-(20)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


3x/21x^2+7x/21x^2-20=0

We multiply all the terms by the denominator


3x+7x-20*21x^2=0

We add all the numbers together, and all the variables

10x-20*21x^2=0

Wy multiply elements

-420x^2+10x=0

a = -420; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-420)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-420}=\frac{-20}{-840}
=1/42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-420}=\frac{0}{-840}
=0
$