(X-2)(x+9)=2x+18

Solution for (X-2)(x+9)=2x+18 equation:

(X-2)(X+9)=2X+18

We move all terms to the left:

(X-2)(X+9)-(2X+18)=0

We get rid of parentheses

(X-2)(X+9)-2X-18=0

We multiply parentheses ..

(+X^2+9X-2X-18)-2X-18=0

We get rid of parentheses

X^2+9X-2X-2X-18-18=0

We add all the numbers together, and all the variables

X^2+5X-36=0

a = 1; b = 5; c = -36;
Δ = b2-4ac
Δ = 52-4·1·(-36)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-13}{2*1}=\frac{-18}{2}
=-9
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+13}{2*1}=\frac{8}{2}
=4
$