x^2=39/49

Solution for x^2=39/49 equation:

x^2=39/49

We move all terms to the left:

x^2-(39/49)=0

We add all the numbers together, and all the variables

x^2-(+39/49)=0

We get rid of parentheses

x^2-39/49=0

We multiply all the terms by the denominator


x^2*49-39=0

Wy multiply elements

49x^2-39=0

a = 49; b = 0; c = -39;
Δ = b2-4ac
Δ = 02-4·49·(-39)
Δ = 7644
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:

$\sqrt{\Delta}=\sqrt{7644}=\sqrt{196*39}=\sqrt{196}*\sqrt{39}=14\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{39}}{2*49}=\frac{0-14\sqrt{39}}{98}
=-\frac{14\sqrt{39}}{98}
=-\frac{\sqrt{39}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{39}}{2*49}=\frac{0+14\sqrt{39}}{98}
=\frac{14\sqrt{39}}{98}
=\frac{\sqrt{39}}{7}
$