400=(30-2x)(24-2x)

Solution for 400=(30-2x)(24-2x) equation:

400=(30-2x)(24-2x)

We move all terms to the left:

400-((30-2x)(24-2x))=0

We add all the numbers together, and all the variables

-((-2x+30)(-2x+24))+400=0

We multiply parentheses ..

-((+4x^2-48x-60x+720))+400=0


We calculate terms in parentheses: -((+4x^2-48x-60x+720)), so:

(+4x^2-48x-60x+720)

We get rid of parentheses

4x^2-48x-60x+720

We add all the numbers together, and all the variables

4x^2-108x+720

Back to the equation:

-(4x^2-108x+720)


We get rid of parentheses

-4x^2+108x-720+400=0

We add all the numbers together, and all the variables

-4x^2+108x-320=0

a = -4; b = 108; c = -320;
Δ = b2-4ac
Δ = 1082-4·(-4)·(-320)
Δ = 6544
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:

$\sqrt{\Delta}=\sqrt{6544}=\sqrt{16*409}=\sqrt{16}*\sqrt{409}=4\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-4\sqrt{409}}{2*-4}=\frac{-108-4\sqrt{409}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+4\sqrt{409}}{2*-4}=\frac{-108+4\sqrt{409}}{-8}
$