3/4x^2=24

Solution for 3/4x^2=24 equation:

3/4x^2=24

We move all terms to the left:

3/4x^2-(24)=0


Domain of the equation: 4x^2!=0

x^2!=0/4

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-24*4x^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}
$