6/4q=7/q+2

Solution for 6/4q=7/q+2 equation:

6/4q=7/q+2

We move all terms to the left:

6/4q-(7/q+2)=0


Domain of the equation: 4q!=0

q!=0/4

q!=0

q∈R



Domain of the equation: q+2)!=0

q∈R


We get rid of parentheses

6/4q-7/q-2=0

We calculate fractions


6q/4q^2+(-28q)/4q^2-2=0

We multiply all the terms by the denominator


6q+(-28q)-2*4q^2=0

Wy multiply elements

-8q^2+6q+(-28q)=0

We get rid of parentheses

-8q^2+6q-28q=0

We add all the numbers together, and all the variables

-8q^2-22q=0

a = -8; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-8)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*-8}=\frac{0}{-16}
=0
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*-8}=\frac{44}{-16}
=-2+3/4
$