1/7x^2-11=0

Solution for 1/7x^2-11=0 equation:

1/7x^2-11=0


Domain of the equation: 7x^2!=0

x^2!=0/7

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-11*7x^2+1=0

Wy multiply elements

-77x^2+1=0

a = -77; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-77)·1
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{77}}{2*-77}=\frac{0-2\sqrt{77}}{-154}
=-\frac{2\sqrt{77}}{-154}
=-\frac{\sqrt{77}}{-77}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{77}}{2*-77}=\frac{0+2\sqrt{77}}{-154}
=\frac{2\sqrt{77}}{-154}
=\frac{\sqrt{77}}{-77}
$