s+31/3s+10=46

Solution for s+31/3s+10=46 equation:

s+31/3s+10=46

We move all terms to the left:

s+31/3s+10-(46)=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-36=0

We multiply all the terms by the denominator


s*3s-36*3s+31=0

Wy multiply elements

3s^2-108s+31=0

a = 3; b = -108; c = +31;
Δ = b2-4ac
Δ = -1082-4·3·31
Δ = 11292
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:

$\sqrt{\Delta}=\sqrt{11292}=\sqrt{4*2823}=\sqrt{4}*\sqrt{2823}=2\sqrt{2823}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-2\sqrt{2823}}{2*3}=\frac{108-2\sqrt{2823}}{6}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+2\sqrt{2823}}{2*3}=\frac{108+2\sqrt{2823}}{6}
$