s+4/2s+10=38

Solution for s+4/2s+10=38 equation:

s+4/2s+10=38

We move all terms to the left:

s+4/2s+10-(38)=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+4/2s-28=0

We multiply all the terms by the denominator


s*2s-28*2s+4=0

Wy multiply elements

2s^2-56s+4=0

a = 2; b = -56; c = +4;
Δ = b2-4ac
Δ = -562-4·2·4
Δ = 3104
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:

$\sqrt{\Delta}=\sqrt{3104}=\sqrt{16*194}=\sqrt{16}*\sqrt{194}=4\sqrt{194}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{194}}{2*2}=\frac{56-4\sqrt{194}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{194}}{2*2}=\frac{56+4\sqrt{194}}{4}
$