35*35-x*x=x*x+25*25

Solution for 35*35-x*x=x*x+25*25 equation:

35*35-x*x=x*x+25*25

We move all terms to the left:

35*35-x*x-(x*x+25*25)=0

We add all the numbers together, and all the variables

-x*x-(x*x+625)+35*35=0

We add all the numbers together, and all the variables

-x*x-(x*x+625)+1225=0

Wy multiply elements

-1x^2-(x*x+625)+1225=0

We get rid of parentheses

-1x^2-x*x-625+1225=0

We add all the numbers together, and all the variables

-1x^2-x*x+600=0

Wy multiply elements

-1x^2-1x^2+600=0

We add all the numbers together, and all the variables

-2x^2+600=0

a = -2; b = 0; c = +600;
Δ = b2-4ac
Δ = 02-4·(-2)·600
Δ = 4800
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:

$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{3}}{2*-2}=\frac{0-40\sqrt{3}}{-4}
=-\frac{40\sqrt{3}}{-4}
=-\frac{10\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{3}}{2*-2}=\frac{0+40\sqrt{3}}{-4}
=\frac{40\sqrt{3}}{-4}
=\frac{10\sqrt{3}}{-1}
$