3/4x^2=6

Solution for 3/4x^2=6 equation:

3/4x^2=6

We move all terms to the left:

3/4x^2-(6)=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


-6*4x^2+3=0

Wy multiply elements

-24x^2+3=0

a = -24; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-24)·3
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*-24}=\frac{0-12\sqrt{2}}{-48}
=-\frac{12\sqrt{2}}{-48}
=-\frac{\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*-24}=\frac{0+12\sqrt{2}}{-48}
=\frac{12\sqrt{2}}{-48}
=\frac{\sqrt{2}}{-4}
$