x2=16/13

Solution for x2=16/13 equation:

x2=16/13

We move all terms to the left:

x2-(16/13)=0

We add all the numbers together, and all the variables

x2-(+16/13)=0

We add all the numbers together, and all the variables

x^2-(+16/13)=0

We get rid of parentheses

x^2-16/13=0

We multiply all the terms by the denominator


x^2*13-16=0

Wy multiply elements

13x^2-16=0

a = 13; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·13·(-16)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{13}}{2*13}=\frac{0-8\sqrt{13}}{26}
=-\frac{8\sqrt{13}}{26}
=-\frac{4\sqrt{13}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{13}}{2*13}=\frac{0+8\sqrt{13}}{26}
=\frac{8\sqrt{13}}{26}
=\frac{4\sqrt{13}}{13}
$