1/10(s)+18=s

Solution for 1/10(s)+18=s equation:

1/10(s)+18=s

We move all terms to the left:

1/10(s)+18-(s)=0


Domain of the equation: 10s!=0

s!=0/10

s!=0

s∈R


We add all the numbers together, and all the variables

-1s+1/10s+18=0

We multiply all the terms by the denominator


-1s*10s+18*10s+1=0

Wy multiply elements

-10s^2+180s+1=0

a = -10; b = 180; c = +1;
Δ = b2-4ac
Δ = 1802-4·(-10)·1
Δ = 32440
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:

$\sqrt{\Delta}=\sqrt{32440}=\sqrt{4*8110}=\sqrt{4}*\sqrt{8110}=2\sqrt{8110}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-2\sqrt{8110}}{2*-10}=\frac{-180-2\sqrt{8110}}{-20}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+2\sqrt{8110}}{2*-10}=\frac{-180+2\sqrt{8110}}{-20}
$