194=3/4x^2

Solution for 194=3/4x^2 equation:

194=3/4x^2

We move all terms to the left:

194-(3/4x^2)=0


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

x!=0/1

x!=0

x∈R


We get rid of parentheses

-3/4x^2+194=0

We multiply all the terms by the denominator


194*4x^2-3=0

Wy multiply elements

776x^2-3=0

a = 776; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·776·(-3)
Δ = 9312
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:

$\sqrt{\Delta}=\sqrt{9312}=\sqrt{16*582}=\sqrt{16}*\sqrt{582}=4\sqrt{582}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{582}}{2*776}=\frac{0-4\sqrt{582}}{1552}
=-\frac{4\sqrt{582}}{1552}
=-\frac{\sqrt{582}}{388}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{582}}{2*776}=\frac{0+4\sqrt{582}}{1552}
=\frac{4\sqrt{582}}{1552}
=\frac{\sqrt{582}}{388}
$