x2=4/21

Solution for x2=4/21 equation:

x2=4/21

We move all terms to the left:

x2-(4/21)=0

We add all the numbers together, and all the variables

x2-(+4/21)=0

We add all the numbers together, and all the variables

x^2-(+4/21)=0

We get rid of parentheses

x^2-4/21=0

We multiply all the terms by the denominator


x^2*21-4=0

Wy multiply elements

21x^2-4=0

a = 21; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·21·(-4)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{21}}{2*21}=\frac{0-4\sqrt{21}}{42}
=-\frac{4\sqrt{21}}{42}
=-\frac{2\sqrt{21}}{21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{21}}{2*21}=\frac{0+4\sqrt{21}}{42}
=\frac{4\sqrt{21}}{42}
=\frac{2\sqrt{21}}{21}
$