2/3a-8=7+1/2a

Solution for 2/3a-8=7+1/2a equation:

2/3a-8=7+1/2a

We move all terms to the left:

2/3a-8-(7+1/2a)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 2a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

2/3a-(1/2a+7)-8=0

We get rid of parentheses

2/3a-1/2a-7-8=0

We calculate fractions


4a/6a^2+(-3a)/6a^2-7-8=0

We add all the numbers together, and all the variables

4a/6a^2+(-3a)/6a^2-15=0

We multiply all the terms by the denominator


4a+(-3a)-15*6a^2=0

Wy multiply elements

-90a^2+4a+(-3a)=0

We get rid of parentheses

-90a^2+4a-3a=0

We add all the numbers together, and all the variables

-90a^2+a=0

a = -90; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-90)·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*-90}=\frac{-2}{-180}
=1/90
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-90}=\frac{0}{-180}
=0
$