(10-x)2-x2=-340

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

(10-x)2-x2=-340

We move all terms to the left:

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

We add all the numbers together, and all the variables

(-1x+10)2-x2-(-340)=0

We add all the numbers together, and all the variables

-1x^2+(-1x+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+360=0

a = -1; b = -2; c = +360;
Δ = b2-4ac
Δ = -22-4·(-1)·360
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-38}{2*-1}=\frac{-36}{-2}
=+18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+38}{2*-1}=\frac{40}{-2}
=-20
$