1/11x^2-77=0

Solution for 1/11x^2-77=0 equation:

1/11x^2-77=0


Domain of the equation: 11x^2!=0

x^2!=0/11

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-77*11x^2+1=0

Wy multiply elements

-847x^2+1=0

a = -847; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-847)·1
Δ = 3388
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:

$\sqrt{\Delta}=\sqrt{3388}=\sqrt{484*7}=\sqrt{484}*\sqrt{7}=22\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{7}}{2*-847}=\frac{0-22\sqrt{7}}{-1694}
=-\frac{22\sqrt{7}}{-1694}
=-\frac{\sqrt{7}}{-77}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{7}}{2*-847}=\frac{0+22\sqrt{7}}{-1694}
=\frac{22\sqrt{7}}{-1694}
=\frac{\sqrt{7}}{-77}
$