(18-2x)(27-2x)=252

Solution for (18-2x)(27-2x)=252 equation:

(18-2x)(27-2x)=252

We move all terms to the left:

(18-2x)(27-2x)-(252)=0

We add all the numbers together, and all the variables

(-2x+18)(-2x+27)-252=0

We multiply parentheses ..

(+4x^2-54x-36x+486)-252=0

We get rid of parentheses

4x^2-54x-36x+486-252=0

We add all the numbers together, and all the variables

4x^2-90x+234=0

a = 4; b = -90; c = +234;
Δ = b2-4ac
Δ = -902-4·4·234
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-66}{2*4}=\frac{24}{8}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+66}{2*4}=\frac{156}{8}
=19+1/2
$