48=3/2*x^2

Solution for 48=3/2*x^2 equation:

48=3/2x^2

We move all terms to the left:

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


Domain of the equation: 2x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-3/2x^2+48=0

We multiply all the terms by the denominator


48*2x^2-3=0

Wy multiply elements

96x^2-3=0

a = 96; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·96·(-3)
Δ = 1152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*96}=\frac{0-24\sqrt{2}}{192}
=-\frac{24\sqrt{2}}{192}
=-\frac{\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*96}=\frac{0+24\sqrt{2}}{192}
=\frac{24\sqrt{2}}{192}
=\frac{\sqrt{2}}{8}
$