14=1/2(3x^2)

Solution for 14=1/2(3x^2) equation:

14=1/2(3x^2)

We move all terms to the left:

14-(1/2(3x^2))=0


Domain of the equation: 23x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-1/23x^2+14=0

We multiply all the terms by the denominator


14*23x^2-1=0

Wy multiply elements

322x^2-1=0

a = 322; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·322·(-1)
Δ = 1288
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:

$\sqrt{\Delta}=\sqrt{1288}=\sqrt{4*322}=\sqrt{4}*\sqrt{322}=2\sqrt{322}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{322}}{2*322}=\frac{0-2\sqrt{322}}{644}
=-\frac{2\sqrt{322}}{644}
=-\frac{\sqrt{322}}{322}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{322}}{2*322}=\frac{0+2\sqrt{322}}{644}
=\frac{2\sqrt{322}}{644}
=\frac{\sqrt{322}}{322}
$