z^2=223/49

Solution for z^2=223/49 equation:

z^2=223/49

We move all terms to the left:

z^2-(223/49)=0

We add all the numbers together, and all the variables

z^2-(+223/49)=0

We get rid of parentheses

z^2-223/49=0

We multiply all the terms by the denominator


z^2*49-223=0

Wy multiply elements

49z^2-223=0

a = 49; b = 0; c = -223;
Δ = b2-4ac
Δ = 02-4·49·(-223)
Δ = 43708
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{43708}=\sqrt{196*223}=\sqrt{196}*\sqrt{223}=14\sqrt{223}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{223}}{2*49}=\frac{0-14\sqrt{223}}{98}
=-\frac{14\sqrt{223}}{98}
=-\frac{\sqrt{223}}{7}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{223}}{2*49}=\frac{0+14\sqrt{223}}{98}
=\frac{14\sqrt{223}}{98}
=\frac{\sqrt{223}}{7}
$