2/8s+5/6s=21

Solution for 2/8s+5/6s=21 equation:

2/8s+5/6s=21

We move all terms to the left:

2/8s+5/6s-(21)=0


Domain of the equation: 8s!=0

s!=0/8

s!=0

s∈R



Domain of the equation: 6s!=0

s!=0/6

s!=0

s∈R


We calculate fractions


12s/48s^2+40s/48s^2-21=0

We multiply all the terms by the denominator


12s+40s-21*48s^2=0

We add all the numbers together, and all the variables

52s-21*48s^2=0

Wy multiply elements

-1008s^2+52s=0

a = -1008; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·(-1008)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*-1008}=\frac{-104}{-2016}
=13/252
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*-1008}=\frac{0}{-2016}
=0
$