a(3/4+a)=21

Solution for a(3/4+a)=21 equation:

a(3/4+a)=21

We move all terms to the left:

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


Domain of the equation: 4+a)!=0

We move all terms containing a to the left, all other terms to the right

a)!=-4

a!=-4/1

a!=-4

a∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

4a^2-21=0

a = 4; b = 0; c = -21;
Δ = b2-4ac
Δ = 02-4·4·(-21)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{21}}{2*4}=\frac{0-4\sqrt{21}}{8}
=-\frac{4\sqrt{21}}{8}
=-\frac{\sqrt{21}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{21}}{2*4}=\frac{0+4\sqrt{21}}{8}
=\frac{4\sqrt{21}}{8}
=\frac{\sqrt{21}}{2}
$