(1/3)(21-3a)=6-a

Solution for (1/3)(21-3a)=6-a equation:

(1/3)(21-3a)=6-a

We move all terms to the left:

(1/3)(21-3a)-(6-a)=0


Domain of the equation: 3)(21-3a)!=0

a∈R


We add all the numbers together, and all the variables

(+1/3)(-3a+21)-(-1a+6)=0

We get rid of parentheses

(+1/3)(-3a+21)+1a-6=0

We multiply parentheses ..

(-3a^2+1/3*21)+1a-6=0

We multiply all the terms by the denominator


(-3a^2+1+1a*3*21)-6*3*21)=0

We add all the numbers together, and all the variables

(-3a^2+1+1a*3*21)=0

We get rid of parentheses

-3a^2+1a*3*21+1=0

Wy multiply elements

-3a^2+63a*2+1=0

Wy multiply elements

-3a^2+126a+1=0

a = -3; b = 126; c = +1;
Δ = b2-4ac
Δ = 1262-4·(-3)·1
Δ = 15888
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:

$\sqrt{\Delta}=\sqrt{15888}=\sqrt{16*993}=\sqrt{16}*\sqrt{993}=4\sqrt{993}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-4\sqrt{993}}{2*-3}=\frac{-126-4\sqrt{993}}{-6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+4\sqrt{993}}{2*-3}=\frac{-126+4\sqrt{993}}{-6}
$