x2=10/19

Solution for x2=10/19 equation:

x2=10/19

We move all terms to the left:

x2-(10/19)=0

We add all the numbers together, and all the variables

x2-(+10/19)=0

We add all the numbers together, and all the variables

x^2-(+10/19)=0

We get rid of parentheses

x^2-10/19=0

We multiply all the terms by the denominator


x^2*19-10=0

Wy multiply elements

19x^2-10=0

a = 19; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·19·(-10)
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{190}}{2*19}=\frac{0-2\sqrt{190}}{38}
=-\frac{2\sqrt{190}}{38}
=-\frac{\sqrt{190}}{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{190}}{2*19}=\frac{0+2\sqrt{190}}{38}
=\frac{2\sqrt{190}}{38}
=\frac{\sqrt{190}}{19}
$