2/3s+4/9s=90

Solution for 2/3s+4/9s=90 equation:

2/3s+4/9s=90

We move all terms to the left:

2/3s+4/9s-(90)=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


18s/27s^2+12s/27s^2-90=0

We multiply all the terms by the denominator


18s+12s-90*27s^2=0

We add all the numbers together, and all the variables

30s-90*27s^2=0

Wy multiply elements

-2430s^2+30s=0

a = -2430; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-2430)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-2430}=\frac{-60}{-4860}
=1/81
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-2430}=\frac{0}{-4860}
=0
$