s+31/4s+10=46

Solution for s+31/4s+10=46 equation:

s+31/4s+10=46

We move all terms to the left:

s+31/4s+10-(46)=0


Domain of the equation: 4s!=0

s!=0/4

s!=0

s∈R


We add all the numbers together, and all the variables

s+31/4s-36=0

We multiply all the terms by the denominator


s*4s-36*4s+31=0

Wy multiply elements

4s^2-144s+31=0

a = 4; b = -144; c = +31;
Δ = b2-4ac
Δ = -1442-4·4·31
Δ = 20240
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:

$\sqrt{\Delta}=\sqrt{20240}=\sqrt{16*1265}=\sqrt{16}*\sqrt{1265}=4\sqrt{1265}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-4\sqrt{1265}}{2*4}=\frac{144-4\sqrt{1265}}{8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+4\sqrt{1265}}{2*4}=\frac{144+4\sqrt{1265}}{8}
$