S(y)=5y/y+7

Solution for S(y)=5y/y+7 equation:

(S)=5S/S+7

We move all terms to the left:

(S)-(5S/S+7)=0


Domain of the equation: S+7)!=0

S∈R


We get rid of parentheses

S-5S/S-7=0

We multiply all the terms by the denominator


S*S-5S-7*S=0

We add all the numbers together, and all the variables

-12S+S*S=0

Wy multiply elements

S^2-12S=0

a = 1; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·1·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*1}=\frac{0}{2}
=0
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*1}=\frac{24}{2}
=12
$