s+31/2s+1010=46

Solution for s+31/2s+1010=46 equation:

s+31/2s+1010=46

We move all terms to the left:

s+31/2s+1010-(46)=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+31/2s+964=0

We multiply all the terms by the denominator


s*2s+964*2s+31=0

Wy multiply elements

2s^2+1928s+31=0

a = 2; b = 1928; c = +31;
Δ = b2-4ac
Δ = 19282-4·2·31
Δ = 3716936
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:

$\sqrt{\Delta}=\sqrt{3716936}=\sqrt{4*929234}=\sqrt{4}*\sqrt{929234}=2\sqrt{929234}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1928)-2\sqrt{929234}}{2*2}=\frac{-1928-2\sqrt{929234}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1928)+2\sqrt{929234}}{2*2}=\frac{-1928+2\sqrt{929234}}{4}
$