3/2x^2-6=0

Solution for 3/2x^2-6=0 equation:

3/2x^2-6=0


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

x^2!=0/2

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-6*2x^2+3=0

Wy multiply elements

-12x^2+3=0

a = -12; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-12)·3
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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