-19=-3/64x^2

Solution for -19=-3/64x^2 equation:

-19=-3/64x^2

We move all terms to the left:

-19-(-3/64x^2)=0


Domain of the equation: 64x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

3/64x^2-19=0

We multiply all the terms by the denominator


-19*64x^2+3=0

Wy multiply elements

-1216x^2+3=0

a = -1216; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-1216)·3
Δ = 14592
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:

$\sqrt{\Delta}=\sqrt{14592}=\sqrt{256*57}=\sqrt{256}*\sqrt{57}=16\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{57}}{2*-1216}=\frac{0-16\sqrt{57}}{-2432}
=-\frac{16\sqrt{57}}{-2432}
=-\frac{\sqrt{57}}{-152}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{57}}{2*-1216}=\frac{0+16\sqrt{57}}{-2432}
=\frac{16\sqrt{57}}{-2432}
=\frac{\sqrt{57}}{-152}
$