1/2q-1/4q=4

Solution for 1/2q-1/4q=4 equation:

1/2q-1/4q=4

We move all terms to the left:

1/2q-1/4q-(4)=0


Domain of the equation: 2q!=0

q!=0/2

q!=0

q∈R



Domain of the equation: 4q!=0

q!=0/4

q!=0

q∈R


We calculate fractions


4q/8q^2+(-2q)/8q^2-4=0

We multiply all the terms by the denominator


4q+(-2q)-4*8q^2=0

Wy multiply elements

-32q^2+4q+(-2q)=0

We get rid of parentheses

-32q^2+4q-2q=0

We add all the numbers together, and all the variables

-32q^2+2q=0

a = -32; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-32)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-32}=\frac{-4}{-64}
=1/16
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-32}=\frac{0}{-64}
=0
$