12-1/2s=20-s

Solution for 12-1/2s=20-s equation:

12-1/2s=20-s

We move all terms to the left:

12-1/2s-(20-s)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

-1/2s-(-1s+20)+12=0

We get rid of parentheses

-1/2s+1s-20+12=0

We multiply all the terms by the denominator


1s*2s-20*2s+12*2s-1=0

Wy multiply elements

2s^2-40s+24s-1=0

We add all the numbers together, and all the variables

2s^2-16s-1=0

a = 2; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·2·(-1)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{66}}{2*2}=\frac{16-2\sqrt{66}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{66}}{2*2}=\frac{16+2\sqrt{66}}{4}
$