s+3+1/2s+10=37

Solution for s+3+1/2s+10=37 equation:

s+3+1/2s+10=37

We move all terms to the left:

s+3+1/2s+10-(37)=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+1/2s-24=0

We multiply all the terms by the denominator


s*2s-24*2s+1=0

Wy multiply elements

2s^2-48s+1=0

a = 2; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·2·1
Δ = 2296
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:

$\sqrt{\Delta}=\sqrt{2296}=\sqrt{4*574}=\sqrt{4}*\sqrt{574}=2\sqrt{574}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{574}}{2*2}=\frac{48-2\sqrt{574}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{574}}{2*2}=\frac{48+2\sqrt{574}}{4}
$