3/4x^2=1000

Solution for 3/4x^2=1000 equation:

3/4x^2=1000

We move all terms to the left:

3/4x^2-(1000)=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


-1000*4x^2+3=0

Wy multiply elements

-4000x^2+3=0

a = -4000; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-4000)·3
Δ = 48000
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:

$\sqrt{\Delta}=\sqrt{48000}=\sqrt{1600*30}=\sqrt{1600}*\sqrt{30}=40\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{30}}{2*-4000}=\frac{0-40\sqrt{30}}{-8000}
=-\frac{40\sqrt{30}}{-8000}
=-\frac{\sqrt{30}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{30}}{2*-4000}=\frac{0+40\sqrt{30}}{-8000}
=\frac{40\sqrt{30}}{-8000}
=\frac{\sqrt{30}}{-200}
$