21-a=3/4a

Solution for 21-a=3/4a equation:

21-a=3/4a

We move all terms to the left:

21-a-(3/4a)=0


Domain of the equation: 4a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

-a-(+3/4a)+21=0

We add all the numbers together, and all the variables

-1a-(+3/4a)+21=0

We get rid of parentheses

-1a-3/4a+21=0

We multiply all the terms by the denominator


-1a*4a+21*4a-3=0

Wy multiply elements

-4a^2+84a-3=0

a = -4; b = 84; c = -3;
Δ = b2-4ac
Δ = 842-4·(-4)·(-3)
Δ = 7008
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:

$\sqrt{\Delta}=\sqrt{7008}=\sqrt{16*438}=\sqrt{16}*\sqrt{438}=4\sqrt{438}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{438}}{2*-4}=\frac{-84-4\sqrt{438}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{438}}{2*-4}=\frac{-84+4\sqrt{438}}{-8}
$