(2x)^2=x^2+6.5^2

Solution for (2x)^2=x^2+6.5^2 equation:

(2x)^2=x^2+6.5^2

We move all terms to the left:

(2x)^2-(x^2+6.5^2)=0

We get rid of parentheses

2x^2-x^2-6.5^2=0

We add all the numbers together, and all the variables

x^2-42.25=0

a = 1; b = 0; c = -42.25;
Δ = b2-4ac
Δ = 02-4·1·(-42.25)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-13}{2*1}=\frac{-13}{2}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+13}{2*1}=\frac{13}{2}
=6+1/2
$