(X)=x^2+6x-40

Solution for (X)=x^2+6x-40 equation:

(X)=X^2+6X-40

We move all terms to the left:

(X)-(X^2+6X-40)=0

We get rid of parentheses

-X^2+X-6X+40=0

We add all the numbers together, and all the variables

-1X^2-5X+40=0

a = -1; b = -5; c = +40;
Δ = b2-4ac
Δ = -52-4·(-1)·40
Δ = 185
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{-(-5)-\sqrt{185}}{2*-1}=\frac{5-\sqrt{185}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{185}}{2*-1}=\frac{5+\sqrt{185}}{-2}
$