224x*x=1

Solution for 224x*x=1 equation:

224x*x=1

We move all terms to the left:

224x*x-(1)=0

Wy multiply elements

224x^2-1=0

a = 224; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·224·(-1)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{14}}{2*224}=\frac{0-8\sqrt{14}}{448}
=-\frac{8\sqrt{14}}{448}
=-\frac{\sqrt{14}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{14}}{2*224}=\frac{0+8\sqrt{14}}{448}
=\frac{8\sqrt{14}}{448}
=\frac{\sqrt{14}}{56}
$