(3/4)(12+4a)=21

Solution for (3/4)(12+4a)=21 equation:

(3/4)(12+4a)=21

We move all terms to the left:

(3/4)(12+4a)-(21)=0


Domain of the equation: 4)(12+4a)!=0

a∈R


We add all the numbers together, and all the variables

(+3/4)(4a+12)-21=0

We multiply parentheses ..

(+12a^2+3/4*12)-21=0

We multiply all the terms by the denominator


(+12a^2+3-21*4*12)=0

We get rid of parentheses

12a^2+3-21*4*12=0

We add all the numbers together, and all the variables

12a^2-1005=0

a = 12; b = 0; c = -1005;
Δ = b2-4ac
Δ = 02-4·12·(-1005)
Δ = 48240
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:

$\sqrt{\Delta}=\sqrt{48240}=\sqrt{144*335}=\sqrt{144}*\sqrt{335}=12\sqrt{335}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{335}}{2*12}=\frac{0-12\sqrt{335}}{24}
=-\frac{12\sqrt{335}}{24}
=-\frac{\sqrt{335}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{335}}{2*12}=\frac{0+12\sqrt{335}}{24}
=\frac{12\sqrt{335}}{24}
=\frac{\sqrt{335}}{2}
$