x^2=49/29

Solution for x^2=49/29 equation:

x^2=49/29

We move all terms to the left:

x^2-(49/29)=0

We add all the numbers together, and all the variables

x^2-(+49/29)=0

We get rid of parentheses

x^2-49/29=0

We multiply all the terms by the denominator


x^2*29-49=0

Wy multiply elements

29x^2-49=0

a = 29; b = 0; c = -49;
Δ = b2-4ac
Δ = 02-4·29·(-49)
Δ = 5684
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:

$\sqrt{\Delta}=\sqrt{5684}=\sqrt{196*29}=\sqrt{196}*\sqrt{29}=14\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{29}}{2*29}=\frac{0-14\sqrt{29}}{58}
=-\frac{14\sqrt{29}}{58}
=-\frac{7\sqrt{29}}{29}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{29}}{2*29}=\frac{0+14\sqrt{29}}{58}
=\frac{14\sqrt{29}}{58}
=\frac{7\sqrt{29}}{29}
$