6s-s-(-4)+5/2s=18

Solution for 6s-s-(-4)+5/2s=18 equation:

6s-s-(-4)+5/2s=18

We move all terms to the left:

6s-s-(-4)+5/2s-(18)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


determiningTheFunctionDomain
6s-s+5/2s-18-(-4)=0

We add all the numbers together, and all the variables

5s+5/2s-14=0

We multiply all the terms by the denominator


5s*2s-14*2s+5=0

Wy multiply elements

10s^2-28s+5=0

a = 10; b = -28; c = +5;
Δ = b2-4ac
Δ = -282-4·10·5
Δ = 584
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:

$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{146}}{2*10}=\frac{28-2\sqrt{146}}{20}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{146}}{2*10}=\frac{28+2\sqrt{146}}{20}
$