2q-6=7/q

Solution for 2q-6=7/q equation:

2q-6=7/q

We move all terms to the left:

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


Domain of the equation: q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2q-7/q-6=0

We multiply all the terms by the denominator


2q*q-6*q-7=0

We add all the numbers together, and all the variables

-6q+2q*q-7=0

Wy multiply elements

2q^2-6q-7=0

a = 2; b = -6; c = -7;
Δ = b2-4ac
Δ = -62-4·2·(-7)
Δ = 92
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{23}}{2*2}=\frac{6-2\sqrt{23}}{4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{23}}{2*2}=\frac{6+2\sqrt{23}}{4}
$