3a^2/3=48a^-2/3

Solution for 3a^2/3=48a^-2/3 equation:

3a^2/3=48a^-2/3

We move all terms to the left:

3a^2/3-(48a^-2/3)=0

We get rid of parentheses

3a^2/3-48a^+2/3=0

We multiply all the terms by the denominator


3a^2-48a^*3+2=0

Wy multiply elements

3a^2-144a+2=0

a = 3; b = -144; c = +2;
Δ = b2-4ac
Δ = -1442-4·3·2
Δ = 20712
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:

$\sqrt{\Delta}=\sqrt{20712}=\sqrt{4*5178}=\sqrt{4}*\sqrt{5178}=2\sqrt{5178}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-2\sqrt{5178}}{2*3}=\frac{144-2\sqrt{5178}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+2\sqrt{5178}}{2*3}=\frac{144+2\sqrt{5178}}{6}
$