560=(24-2x)(18-2x)

Solution for 560=(24-2x)(18-2x) equation:

560=(24-2x)(18-2x)

We move all terms to the left:

560-((24-2x)(18-2x))=0

We add all the numbers together, and all the variables

-((-2x+24)(-2x+18))+560=0

We multiply parentheses ..

-((+4x^2-36x-48x+432))+560=0


We calculate terms in parentheses: -((+4x^2-36x-48x+432)), so:

(+4x^2-36x-48x+432)

We get rid of parentheses

4x^2-36x-48x+432

We add all the numbers together, and all the variables

4x^2-84x+432

Back to the equation:

-(4x^2-84x+432)


We get rid of parentheses

-4x^2+84x-432+560=0

We add all the numbers together, and all the variables

-4x^2+84x+128=0

a = -4; b = 84; c = +128;
Δ = b2-4ac
Δ = 842-4·(-4)·128
Δ = 9104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9104}=\sqrt{16*569}=\sqrt{16}*\sqrt{569}=4\sqrt{569}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{569}}{2*-4}=\frac{-84-4\sqrt{569}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{569}}{2*-4}=\frac{-84+4\sqrt{569}}{-8}
$