(x-5)(x+3)=200

Solution for (x-5)(x+3)=200 equation:

(x-5)(x+3)=200

We move all terms to the left:

(x-5)(x+3)-(200)=0

We multiply parentheses ..

(+x^2+3x-5x-15)-200=0

We get rid of parentheses

x^2+3x-5x-15-200=0

We add all the numbers together, and all the variables

x^2-2x-215=0

a = 1; b = -2; c = -215;
Δ = b2-4ac
Δ = -22-4·1·(-215)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-12\sqrt{6}}{2*1}=\frac{2-12\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+12\sqrt{6}}{2*1}=\frac{2+12\sqrt{6}}{2}
$