-1/3x+7x=-20

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

-1/3x+7x=-20

We move all terms to the left:

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

We multiply all the terms by the denominator


7x*3x+20*3x-1=0

Wy multiply elements

21x^2+60x-1=0

a = 21; b = 60; c = -1;
Δ = b2-4ac
Δ = 602-4·21·(-1)
Δ = 3684
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3684}=\sqrt{4*921}=\sqrt{4}*\sqrt{921}=2\sqrt{921}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{921}}{2*21}=\frac{-60-2\sqrt{921}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{921}}{2*21}=\frac{-60+2\sqrt{921}}{42}
$