(40-2x)(24-2x)=1457

Solution for (40-2x)(24-2x)=1457 equation:

(40-2x)(24-2x)=1457

We move all terms to the left:

(40-2x)(24-2x)-(1457)=0

We add all the numbers together, and all the variables

(-2x+40)(-2x+24)-1457=0

We multiply parentheses ..

(+4x^2-48x-80x+960)-1457=0

We get rid of parentheses

4x^2-48x-80x+960-1457=0

We add all the numbers together, and all the variables

4x^2-128x-497=0

a = 4; b = -128; c = -497;
Δ = b2-4ac
Δ = -1282-4·4·(-497)
Δ = 24336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24336}=156$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-156}{2*4}=\frac{-28}{8}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+156}{2*4}=\frac{284}{8}
=35+1/2
$