X=x^2+11x+24

Solution for X=x^2+11x+24 equation:

X=X^2+11X+24

We move all terms to the left:

X-(X^2+11X+24)=0

We get rid of parentheses

-X^2+X-11X-24=0

We add all the numbers together, and all the variables

-1X^2-10X-24=0

a = -1; b = -10; c = -24;
Δ = b2-4ac
Δ = -102-4·(-1)·(-24)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*-1}=\frac{8}{-2}
=-4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*-1}=\frac{12}{-2}
=-6
$