33-3/4a=2a

Solution for 33-3/4a=2a equation:

33-3/4a=2a

We move all terms to the left:

33-3/4a-(2a)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We add all the numbers together, and all the variables

-2a-3/4a+33=0

We multiply all the terms by the denominator


-2a*4a+33*4a-3=0

Wy multiply elements

-8a^2+132a-3=0

a = -8; b = 132; c = -3;
Δ = b2-4ac
Δ = 1322-4·(-8)·(-3)
Δ = 17328
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:

$\sqrt{\Delta}=\sqrt{17328}=\sqrt{5776*3}=\sqrt{5776}*\sqrt{3}=76\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-76\sqrt{3}}{2*-8}=\frac{-132-76\sqrt{3}}{-16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+76\sqrt{3}}{2*-8}=\frac{-132+76\sqrt{3}}{-16}
$