1/3s+2/9s=10

Solution for 1/3s+2/9s=10 equation:

1/3s+2/9s=10

We move all terms to the left:

1/3s+2/9s-(10)=0


Domain of the equation: 3s!=0

s!=0/3

s!=0

s∈R



Domain of the equation: 9s!=0

s!=0/9

s!=0

s∈R


We calculate fractions


9s/27s^2+6s/27s^2-10=0

We multiply all the terms by the denominator


9s+6s-10*27s^2=0

We add all the numbers together, and all the variables

15s-10*27s^2=0

Wy multiply elements

-270s^2+15s=0

a = -270; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-270)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-270}=\frac{-30}{-540}
=1/18
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-270}=\frac{0}{-540}
=0
$