-5/(2s)-1s=10

Solution for -5/(2s)-1s=10 equation:

-5/(2s)-1s=10

We move all terms to the left:

-5/(2s)-1s-(10)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

-1s-5/2s-10=0

We multiply all the terms by the denominator


-1s*2s-10*2s-5=0

Wy multiply elements

-2s^2-20s-5=0

a = -2; b = -20; c = -5;
Δ = b2-4ac
Δ = -202-4·(-2)·(-5)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-6\sqrt{10}}{2*-2}=\frac{20-6\sqrt{10}}{-4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+6\sqrt{10}}{2*-2}=\frac{20+6\sqrt{10}}{-4}
$