3/2x^2-12=21

Solution for 3/2x^2-12=21 equation:

3/2x^2-12=21

We move all terms to the left:

3/2x^2-12-(21)=0


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

x^2!=0/2

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x^2-33=0

We multiply all the terms by the denominator


-33*2x^2+3=0

Wy multiply elements

-66x^2+3=0

a = -66; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-66)·3
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{22}}{2*-66}=\frac{0-6\sqrt{22}}{-132}
=-\frac{6\sqrt{22}}{-132}
=-\frac{\sqrt{22}}{-22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{22}}{2*-66}=\frac{0+6\sqrt{22}}{-132}
=\frac{6\sqrt{22}}{-132}
=\frac{\sqrt{22}}{-22}
$