21+2a=3(25/6a+1)

Solution for 21+2a=3(25/6a+1) equation:

21+2a=3(25/6a+1)

We move all terms to the left:

21+2a-(3(25/6a+1))=0


Domain of the equation: 6a+1))!=0

a∈R


We multiply all the terms by the denominator


2a*6a+21*6a+1))-(3(25+1))=0

We add all the numbers together, and all the variables

2a*6a+21*6a+1))-(326)=0

We add all the numbers together, and all the variables

2a*6a+21*6a=0

Wy multiply elements

12a^2+126a=0

a = 12; b = 126; c = 0;
Δ = b2-4ac
Δ = 1262-4·12·0
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-126}{2*12}=\frac{-252}{24}
=-10+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+126}{2*12}=\frac{0}{24}
=0
$