s+7/2s+20=47

Solution for s+7/2s+20=47 equation:

s+7/2s+20=47

We move all terms to the left:

s+7/2s+20-(47)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

s+7/2s-27=0

We multiply all the terms by the denominator


s*2s-27*2s+7=0

Wy multiply elements

2s^2-54s+7=0

a = 2; b = -54; c = +7;
Δ = b2-4ac
Δ = -542-4·2·7
Δ = 2860
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:

$\sqrt{\Delta}=\sqrt{2860}=\sqrt{4*715}=\sqrt{4}*\sqrt{715}=2\sqrt{715}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{715}}{2*2}=\frac{54-2\sqrt{715}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{715}}{2*2}=\frac{54+2\sqrt{715}}{4}
$