(30-2x)(40-2x)=416

Solution for (30-2x)(40-2x)=416 equation:

(30-2x)(40-2x)=416

We move all terms to the left:

(30-2x)(40-2x)-(416)=0

We add all the numbers together, and all the variables

(-2x+30)(-2x+40)-416=0

We multiply parentheses ..

(+4x^2-80x-60x+1200)-416=0

We get rid of parentheses

4x^2-80x-60x+1200-416=0

We add all the numbers together, and all the variables

4x^2-140x+784=0

a = 4; b = -140; c = +784;
Δ = b2-4ac
Δ = -1402-4·4·784
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-84}{2*4}=\frac{56}{8}
=7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+84}{2*4}=\frac{224}{8}
=28
$