4/5s+1/3s=2/45

Solution for 4/5s+1/3s=2/45 equation:

4/5s+1/3s=2/45

We move all terms to the left:

4/5s+1/3s-(2/45)=0


Domain of the equation: 5s!=0

s!=0/5

s!=0

s∈R



Domain of the equation: 3s!=0

s!=0/3

s!=0

s∈R


We add all the numbers together, and all the variables

4/5s+1/3s-(+2/45)=0

We get rid of parentheses

4/5s+1/3s-2/45=0

We calculate fractions


(-90s^2)/2700s^2+2160s/2700s^2+900s/2700s^2=0

We multiply all the terms by the denominator


(-90s^2)+2160s+900s=0

We add all the numbers together, and all the variables

(-90s^2)+3060s=0

We get rid of parentheses

-90s^2+3060s=0

a = -90; b = 3060; c = 0;
Δ = b2-4ac
Δ = 30602-4·(-90)·0
Δ = 9363600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9363600}=3060$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3060)-3060}{2*-90}=\frac{-6120}{-180}
=+34
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3060)+3060}{2*-90}=\frac{0}{-180}
=0
$