(X)=-x^2-2x+15

Solution for (X)=-x^2-2x+15 equation:

(X)=-X^2-2X+15

We move all terms to the left:

(X)-(-X^2-2X+15)=0

We get rid of parentheses

X^2+2X+X-15=0

We add all the numbers together, and all the variables

X^2+3X-15=0

a = 1; b = 3; c = -15;
Δ = b2-4ac
Δ = 32-4·1·(-15)
Δ = 69
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{69}}{2*1}=\frac{-3-\sqrt{69}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{69}}{2*1}=\frac{-3+\sqrt{69}}{2}
$