1/4q+-7=8-1/2q

Solution for 1/4q+-7=8-1/2q equation:

1/4q+-7=8-1/2q

We move all terms to the left:

1/4q+-7-(8-1/2q)=0


Domain of the equation: 4q!=0

q!=0/4

q!=0

q∈R



Domain of the equation: 2q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

1/4q-(-1/2q+8)-7+=0

We add all the numbers together, and all the variables

1/4q-(-1/2q+8)=0

We get rid of parentheses

1/4q+1/2q-8=0

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

6q-8*8q^2=0

Wy multiply elements

-64q^2+6q=0

a = -64; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-64)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-64}=\frac{-12}{-128}
=3/32
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-64}=\frac{0}{-128}
=0
$