x2=49/69

Solution for x2=49/69 equation:

x2=49/69

We move all terms to the left:

x2-(49/69)=0

We add all the numbers together, and all the variables

x2-(+49/69)=0

We add all the numbers together, and all the variables

x^2-(+49/69)=0

We get rid of parentheses

x^2-49/69=0

We multiply all the terms by the denominator


x^2*69-49=0

Wy multiply elements

69x^2-49=0

a = 69; b = 0; c = -49;
Δ = b2-4ac
Δ = 02-4·69·(-49)
Δ = 13524
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:

$\sqrt{\Delta}=\sqrt{13524}=\sqrt{196*69}=\sqrt{196}*\sqrt{69}=14\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{69}}{2*69}=\frac{0-14\sqrt{69}}{138}
=-\frac{14\sqrt{69}}{138}
=-\frac{7\sqrt{69}}{69}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{69}}{2*69}=\frac{0+14\sqrt{69}}{138}
=\frac{14\sqrt{69}}{138}
=\frac{7\sqrt{69}}{69}
$