2/3s+5/6s=20

Solution for 2/3s+5/6s=20 equation:

2/3s+5/6s=20

We move all terms to the left:

2/3s+5/6s-(20)=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^2-20=0

We multiply all the terms by the denominator


12s+15s-20*18s^2=0

We add all the numbers together, and all the variables

27s-20*18s^2=0

Wy multiply elements

-360s^2+27s=0

a = -360; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-360)·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*-360}=\frac{-54}{-720}
=3/40
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-360}=\frac{0}{-720}
=0
$