((X^2)+2x-24)=(3x+6)

Solution for ((X^2)+2x-24)=(3x+6) equation:

((X^2)+2X-24)=(3X+6)

We move all terms to the left:

((X^2)+2X-24)-((3X+6))=0

We get rid of parentheses

X^2+2X-((3X+6))-24=0


We calculate terms in parentheses: -((3X+6)), so:

(3X+6)

We get rid of parentheses

3X+6

Back to the equation:

-(3X+6)


We get rid of parentheses

X^2+2X-3X-6-24=0

We add all the numbers together, and all the variables

X^2-1X-30=0

a = 1; b = -1; c = -30;
Δ = b2-4ac
Δ = -12-4·1·(-30)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*1}=\frac{-10}{2}
=-5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*1}=\frac{12}{2}
=6
$