(1/9)s=5/4

Solution for (1/9)s=5/4 equation:

(1/9)s=5/4

We move all terms to the left:

(1/9)s-(5/4)=0


Domain of the equation: 9)s!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

(+1/9)s-(+5/4)=0

We multiply parentheses

s^2-(+5/4)=0

We get rid of parentheses

s^2-5/4=0

We multiply all the terms by the denominator


s^2*4-5=0

Wy multiply elements

4s^2-5=0

a = 4; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·4·(-5)
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*4}=\frac{0-4\sqrt{5}}{8}
=-\frac{4\sqrt{5}}{8}
=-\frac{\sqrt{5}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*4}=\frac{0+4\sqrt{5}}{8}
=\frac{4\sqrt{5}}{8}
=\frac{\sqrt{5}}{2}
$