-7+a=13-2/3a

Solution for -7+a=13-2/3a equation:

-7+a=13-2/3a

We move all terms to the left:

-7+a-(13-2/3a)=0


Domain of the equation: 3a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

a-(-2/3a+13)-7=0

We get rid of parentheses

a+2/3a-13-7=0

We multiply all the terms by the denominator


a*3a-13*3a-7*3a+2=0

Wy multiply elements

3a^2-39a-21a+2=0

We add all the numbers together, and all the variables

3a^2-60a+2=0

a = 3; b = -60; c = +2;
Δ = b2-4ac
Δ = -602-4·3·2
Δ = 3576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3576}=\sqrt{4*894}=\sqrt{4}*\sqrt{894}=2\sqrt{894}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{894}}{2*3}=\frac{60-2\sqrt{894}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{894}}{2*3}=\frac{60+2\sqrt{894}}{6}
$