s+31/3s+10=55

Solution for s+31/3s+10=55 equation:

s+31/3s+10=55

We move all terms to the left:

s+31/3s+10-(55)=0


Domain of the equation: 3s!=0

s!=0/3

s!=0

s∈R


We add all the numbers together, and all the variables

s+31/3s-45=0

We multiply all the terms by the denominator


s*3s-45*3s+31=0

Wy multiply elements

3s^2-135s+31=0

a = 3; b = -135; c = +31;
Δ = b2-4ac
Δ = -1352-4·3·31
Δ = 17853
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-\sqrt{17853}}{2*3}=\frac{135-\sqrt{17853}}{6}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+\sqrt{17853}}{2*3}=\frac{135+\sqrt{17853}}{6}
$