1/2(a)-7=2/3(a)-9

Solution for 1/2(a)-7=2/3(a)-9 equation:

1/2(a)-7=2/3(a)-9

We move all terms to the left:

1/2(a)-7-(2/3(a)-9)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 3a-9)!=0

a∈R


We get rid of parentheses

1/2a-2/3a+9-7=0

We calculate fractions


3a/6a^2+(-4a)/6a^2+9-7=0

We add all the numbers together, and all the variables

3a/6a^2+(-4a)/6a^2+2=0

We multiply all the terms by the denominator


3a+(-4a)+2*6a^2=0

Wy multiply elements

12a^2+3a+(-4a)=0

We get rid of parentheses

12a^2+3a-4a=0

We add all the numbers together, and all the variables

12a^2-1a=0

a = 12; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·12·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*12}=\frac{0}{24}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*12}=\frac{2}{24}
=1/12
$