x^2-9/14+1/14=0

Solution for x^2-9/14+1/14=0 equation:

x^2-9/14+1/14=0

We multiply all the terms by the denominator


x^2*14-9+1=0

We add all the numbers together, and all the variables

x^2*14-8=0

Wy multiply elements

14x^2-8=0

a = 14; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·14·(-8)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{7}}{2*14}=\frac{0-8\sqrt{7}}{28}
=-\frac{8\sqrt{7}}{28}
=-\frac{2\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{7}}{2*14}=\frac{0+8\sqrt{7}}{28}
=\frac{8\sqrt{7}}{28}
=\frac{2\sqrt{7}}{7}
$