(x-10)2-x2=-340

Solution for (x-10)2-x2=-340 equation:

(x-10)2-x2=-340

We move all terms to the left:

(x-10)2-x2-(-340)=0

We add all the numbers together, and all the variables

-1x^2+(x-10)2+340=0

We multiply parentheses

-1x^2+2x-20+340=0

We add all the numbers together, and all the variables

-1x^2+2x+320=0

a = -1; b = 2; c = +320;
Δ = b2-4ac
Δ = 22-4·(-1)·320
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{321}}{2*-1}=\frac{-2-2\sqrt{321}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{321}}{2*-1}=\frac{-2+2\sqrt{321}}{-2}
$