(5-a)*(-2-a)-18=0

Solution for (5-a)*(-2-a)-18=0 equation:

(5-a)(-2-a)-18=0

We add all the numbers together, and all the variables

(-1a+5)(-1a-2)-18=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

a^2-3a-28=0

a = 1; b = -3; c = -28;
Δ = b2-4ac
Δ = -32-4·1·(-28)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-11}{2*1}=\frac{-8}{2}
=-4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+11}{2*1}=\frac{14}{2}
=7
$