1/2(q)=9-2/3(q)

Solution for 1/2(q)=9-2/3(q) equation:

1/2(q)=9-2/3(q)

We move all terms to the left:

1/2(q)-(9-2/3(q))=0


Domain of the equation: 2q!=0

q!=0/2

q!=0

q∈R



Domain of the equation: 3q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

1/2q-(-2/3q+9)=0

We get rid of parentheses

1/2q+2/3q-9=0

We calculate fractions


3q/6q^2+4q/6q^2-9=0

We multiply all the terms by the denominator


3q+4q-9*6q^2=0

We add all the numbers together, and all the variables

7q-9*6q^2=0

Wy multiply elements

-54q^2+7q=0

a = -54; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-54)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-54}=\frac{-14}{-108}
=7/54
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-54}=\frac{0}{-108}
=0
$