(10*10)+(20*20)=(c*c)

Solution for (10*10)+(20*20)=(c*c) equation:

(10*10)+(20*20)=(c*c)

We move all terms to the left:

(10*10)+(20*20)-((c*c))=0

We add all the numbers together, and all the variables

-((+c*c))+100+400=0

We add all the numbers together, and all the variables

-((+c*c))+500=0


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

(+c*c)

We get rid of parentheses

c*c

Wy multiply elements

c^2

Back to the equation:

-(c^2)


We add all the numbers together, and all the variables

-1c^2+500=0

a = -1; b = 0; c = +500;
Δ = b2-4ac
Δ = 02-4·(-1)·500
Δ = 2000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{5}}{2*-1}=\frac{0-20\sqrt{5}}{-2}
=-\frac{20\sqrt{5}}{-2}
=-\frac{10\sqrt{5}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{5}}{2*-1}=\frac{0+20\sqrt{5}}{-2}
=\frac{20\sqrt{5}}{-2}
=\frac{10\sqrt{5}}{-1}
$