1/2(3x^2)=96

Solution for 1/2(3x^2)=96 equation:

1/2(3x^2)=96

We move all terms to the left:

1/2(3x^2)-(96)=0


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

x^2!=0/23

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-96*23x^2+1=0

Wy multiply elements

-2208x^2+1=0

a = -2208; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-2208)·1
Δ = 8832
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:

$\sqrt{\Delta}=\sqrt{8832}=\sqrt{64*138}=\sqrt{64}*\sqrt{138}=8\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{138}}{2*-2208}=\frac{0-8\sqrt{138}}{-4416}
=-\frac{8\sqrt{138}}{-4416}
=-\frac{\sqrt{138}}{-552}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{138}}{2*-2208}=\frac{0+8\sqrt{138}}{-4416}
=\frac{8\sqrt{138}}{-4416}
=\frac{\sqrt{138}}{-552}
$