x^2=65/49

Solution for x^2=65/49 equation:

x^2=65/49

We move all terms to the left:

x^2-(65/49)=0

We add all the numbers together, and all the variables

x^2-(+65/49)=0

We get rid of parentheses

x^2-65/49=0

We multiply all the terms by the denominator


x^2*49-65=0

Wy multiply elements

49x^2-65=0

a = 49; b = 0; c = -65;
Δ = b2-4ac
Δ = 02-4·49·(-65)
Δ = 12740
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:

$\sqrt{\Delta}=\sqrt{12740}=\sqrt{196*65}=\sqrt{196}*\sqrt{65}=14\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{65}}{2*49}=\frac{0-14\sqrt{65}}{98}
=-\frac{14\sqrt{65}}{98}
=-\frac{\sqrt{65}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{65}}{2*49}=\frac{0+14\sqrt{65}}{98}
=\frac{14\sqrt{65}}{98}
=\frac{\sqrt{65}}{7}
$