2/3s+5/6s=21

Solution for 2/3s+5/6s=21 equation:

2/3s+5/6s=21

We move all terms to the left:

2/3s+5/6s-(21)=0


Domain of the equation: 3s!=0

s!=0/3

s!=0

s∈R



Domain of the equation: 6s!=0

s!=0/6

s!=0

s∈R


We calculate fractions


12s/18s^2+15s/18s^2-21=0

We multiply all the terms by the denominator


12s+15s-21*18s^2=0

We add all the numbers together, and all the variables

27s-21*18s^2=0

Wy multiply elements

-378s^2+27s=0

a = -378; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-378)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-378}=\frac{-54}{-756}
=1/14
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-378}=\frac{0}{-756}
=0
$