s+2+1/2s+10=45

Solution for s+2+1/2s+10=45 equation:

s+2+1/2s+10=45

We move all terms to the left:

s+2+1/2s+10-(45)=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-33=0

We multiply all the terms by the denominator


s*2s-33*2s+1=0

Wy multiply elements

2s^2-66s+1=0

a = 2; b = -66; c = +1;
Δ = b2-4ac
Δ = -662-4·2·1
Δ = 4348
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:

$\sqrt{\Delta}=\sqrt{4348}=\sqrt{4*1087}=\sqrt{4}*\sqrt{1087}=2\sqrt{1087}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1087}}{2*2}=\frac{66-2\sqrt{1087}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1087}}{2*2}=\frac{66+2\sqrt{1087}}{4}
$