3/4a=a+6

Solution for 3/4a=a+6 equation:

3/4a=a+6

We move all terms to the left:

3/4a-(a+6)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We get rid of parentheses

3/4a-a-6=0

We multiply all the terms by the denominator


-a*4a-6*4a+3=0

Wy multiply elements

-4a^2-24a+3=0

a = -4; b = -24; c = +3;
Δ = b2-4ac
Δ = -242-4·(-4)·3
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{39}}{2*-4}=\frac{24-4\sqrt{39}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{39}}{2*-4}=\frac{24+4\sqrt{39}}{-8}
$