s+3*1/2s+10=55

Solution for s+3*1/2s+10=55 equation:

s+3*1/2s+10=55

We move all terms to the left:

s+3*1/2s+10-(55)=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+3*1/2s-45=0

We multiply all the terms by the denominator


s*2s-45*2s+3*1=0

We add all the numbers together, and all the variables

s*2s-45*2s+3=0

Wy multiply elements

2s^2-90s+3=0

a = 2; b = -90; c = +3;
Δ = b2-4ac
Δ = -902-4·2·3
Δ = 8076
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:

$\sqrt{\Delta}=\sqrt{8076}=\sqrt{4*2019}=\sqrt{4}*\sqrt{2019}=2\sqrt{2019}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2019}}{2*2}=\frac{90-2\sqrt{2019}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2019}}{2*2}=\frac{90+2\sqrt{2019}}{4}
$