3/4s+3/8s=1/2

Solution for 3/4s+3/8s=1/2 equation:

3/4s+3/8s=1/2

We move all terms to the left:

3/4s+3/8s-(1/2)=0


Domain of the equation: 4s!=0

s!=0/4

s!=0

s∈R



Domain of the equation: 8s!=0

s!=0/8

s!=0

s∈R


We add all the numbers together, and all the variables

3/4s+3/8s-(+1/2)=0

We get rid of parentheses

3/4s+3/8s-1/2=0

We calculate fractions


(-256s^2)/128s^2+96s/128s^2+48s/128s^2=0

We multiply all the terms by the denominator


(-256s^2)+96s+48s=0

We add all the numbers together, and all the variables

(-256s^2)+144s=0

We get rid of parentheses

-256s^2+144s=0

a = -256; b = 144; c = 0;
Δ = b2-4ac
Δ = 1442-4·(-256)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-144}{2*-256}=\frac{-288}{-512}
=9/16
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144}{2*-256}=\frac{0}{-512}
=0
$