-1/7x=-3x+20

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

-1/7x=-3x+20

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

21x^2-140x-1=0

a = 21; b = -140; c = -1;
Δ = b2-4ac
Δ = -1402-4·21·(-1)
Δ = 19684
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:

$\sqrt{\Delta}=\sqrt{19684}=\sqrt{4*4921}=\sqrt{4}*\sqrt{4921}=2\sqrt{4921}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-2\sqrt{4921}}{2*21}=\frac{140-2\sqrt{4921}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+2\sqrt{4921}}{2*21}=\frac{140+2\sqrt{4921}}{42}
$