3/7s=130-s

Solution for 3/7s=130-s equation:

3/7s=130-s

We move all terms to the left:

3/7s-(130-s)=0


Domain of the equation: 7s!=0

s!=0/7

s!=0

s∈R


We add all the numbers together, and all the variables

3/7s-(-1s+130)=0

We get rid of parentheses

3/7s+1s-130=0

We multiply all the terms by the denominator


1s*7s-130*7s+3=0

Wy multiply elements

7s^2-910s+3=0

a = 7; b = -910; c = +3;
Δ = b2-4ac
Δ = -9102-4·7·3
Δ = 828016
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:

$\sqrt{\Delta}=\sqrt{828016}=\sqrt{16*51751}=\sqrt{16}*\sqrt{51751}=4\sqrt{51751}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-910)-4\sqrt{51751}}{2*7}=\frac{910-4\sqrt{51751}}{14}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-910)+4\sqrt{51751}}{2*7}=\frac{910+4\sqrt{51751}}{14}
$