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

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

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

We move all terms to the left:

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


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R



Domain of the equation: 4s!=0

s!=0/4

s!=0

s∈R


We calculate fractions


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

We multiply all the terms by the denominator


4s+(2s+3)-4*8s^2=0

Wy multiply elements

-32s^2+4s+(2s+3)=0

We get rid of parentheses

-32s^2+4s+2s+3=0

We add all the numbers together, and all the variables

-32s^2+6s+3=0

a = -32; b = 6; c = +3;
Δ = b2-4ac
Δ = 62-4·(-32)·3
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{105}}{2*-32}=\frac{-6-2\sqrt{105}}{-64}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{105}}{2*-32}=\frac{-6+2\sqrt{105}}{-64}
$