(3/4)s+(1/5)s=4/5

Solution for (3/4)s+(1/5)s=4/5 equation:

(3/4)s+(1/5)s=4/5

We move all terms to the left:

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


Domain of the equation: 4)s!=0

s!=0/1

s!=0

s∈R



Domain of the equation: 5)s!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

3s^2+s^2-4/5=0

We multiply all the terms by the denominator


3s^2*5+s^2*5-4=0

Wy multiply elements

15s^2+5s^2-4=0

We add all the numbers together, and all the variables

20s^2-4=0

a = 20; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·20·(-4)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{5}}{2*20}=\frac{0-8\sqrt{5}}{40}
=-\frac{8\sqrt{5}}{40}
=-\frac{\sqrt{5}}{5}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{5}}{2*20}=\frac{0+8\sqrt{5}}{40}
=\frac{8\sqrt{5}}{40}
=\frac{\sqrt{5}}{5}
$