(18-x)(13-x)=66

Solution for (18-x)(13-x)=66 equation:

(18-x)(13-x)=66

We move all terms to the left:

(18-x)(13-x)-(66)=0

We add all the numbers together, and all the variables

(-1x+18)(-1x+13)-66=0

We multiply parentheses ..

(+x^2-13x-18x+234)-66=0

We get rid of parentheses

x^2-13x-18x+234-66=0

We add all the numbers together, and all the variables

x^2-31x+168=0

a = 1; b = -31; c = +168;
Δ = b2-4ac
Δ = -312-4·1·168
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-17}{2*1}=\frac{14}{2}
=7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+17}{2*1}=\frac{48}{2}
=24
$