1/2s+3/4s=16

Solution for 1/2s+3/4s=16 equation:

1/2s+3/4s=16

We move all terms to the left:

1/2s+3/4s-(16)=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+6s/8s^2-16=0

We multiply all the terms by the denominator


4s+6s-16*8s^2=0

We add all the numbers together, and all the variables

10s-16*8s^2=0

Wy multiply elements

-128s^2+10s=0

a = -128; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-128)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-128}=\frac{-20}{-256}
=5/64
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-128}=\frac{0}{-256}
=0
$