x2=6/19

Solution for x2=6/19 equation:

x2=6/19

We move all terms to the left:

x2-(6/19)=0

We add all the numbers together, and all the variables

x2-(+6/19)=0

We add all the numbers together, and all the variables

x^2-(+6/19)=0

We get rid of parentheses

x^2-6/19=0

We multiply all the terms by the denominator


x^2*19-6=0

Wy multiply elements

19x^2-6=0

a = 19; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·19·(-6)
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{114}}{2*19}=\frac{0-2\sqrt{114}}{38}
=-\frac{2\sqrt{114}}{38}
=-\frac{\sqrt{114}}{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{114}}{2*19}=\frac{0+2\sqrt{114}}{38}
=\frac{2\sqrt{114}}{38}
=\frac{\sqrt{114}}{19}
$