1/3s=7s=

Solution for 1/3s=7s= equation:

1/3s=7s=

We move all terms to the left:

1/3s-(7s)=0


Domain of the equation: 3s!=0

s!=0/3

s!=0

s∈R


We add all the numbers together, and all the variables

-7s+1/3s=0

We multiply all the terms by the denominator


-7s*3s+1=0

Wy multiply elements

-21s^2+1=0

a = -21; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-21)·1
Δ = 84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*-21}=\frac{0-2\sqrt{21}}{-42}
=-\frac{2\sqrt{21}}{-42}
=-\frac{\sqrt{21}}{-21}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*-21}=\frac{0+2\sqrt{21}}{-42}
=\frac{2\sqrt{21}}{-42}
=\frac{\sqrt{21}}{-21}
$