(X+5)(x+2)=18

Solution for (X+5)(x+2)=18 equation:

(X+5)(X+2)=18

We move all terms to the left:

(X+5)(X+2)-(18)=0

We multiply parentheses ..

(+X^2+2X+5X+10)-18=0

We get rid of parentheses

X^2+2X+5X+10-18=0

We add all the numbers together, and all the variables

X^2+7X-8=0

a = 1; b = 7; c = -8;
Δ = b2-4ac
Δ = 72-4·1·(-8)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-9}{2*1}=\frac{-16}{2}
=-8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+9}{2*1}=\frac{2}{2}
=1
$