(21*21)+(17*17)=(x*x)

Solution for (21*21)+(17*17)=(x*x) equation:

(21*21)+(17*17)=(x*x)

We move all terms to the left:

(21*21)+(17*17)-((x*x))=0

We add all the numbers together, and all the variables

-((+x*x))+441+289=0

We add all the numbers together, and all the variables

-((+x*x))+730=0


We calculate terms in parentheses: -((+x*x)), so:

(+x*x)

We get rid of parentheses

x*x

Wy multiply elements

x^2

Back to the equation:

-(x^2)


We add all the numbers together, and all the variables

-1x^2+730=0

a = -1; b = 0; c = +730;
Δ = b2-4ac
Δ = 02-4·(-1)·730
Δ = 2920
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:

$\sqrt{\Delta}=\sqrt{2920}=\sqrt{4*730}=\sqrt{4}*\sqrt{730}=2\sqrt{730}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{730}}{2*-1}=\frac{0-2\sqrt{730}}{-2}
=-\frac{2\sqrt{730}}{-2}
=-\frac{\sqrt{730}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{730}}{2*-1}=\frac{0+2\sqrt{730}}{-2}
=\frac{2\sqrt{730}}{-2}
=\frac{\sqrt{730}}{-1}
$