(19-2x)(26-2x)=408

Solution for (19-2x)(26-2x)=408 equation:

(19-2x)(26-2x)=408

We move all terms to the left:

(19-2x)(26-2x)-(408)=0

We add all the numbers together, and all the variables

(-2x+19)(-2x+26)-408=0

We multiply parentheses ..

(+4x^2-52x-38x+494)-408=0

We get rid of parentheses

4x^2-52x-38x+494-408=0

We add all the numbers together, and all the variables

4x^2-90x+86=0

a = 4; b = -90; c = +86;
Δ = b2-4ac
Δ = -902-4·4·86
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-82}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+82}{2*4}=\frac{172}{8}
=21+1/2
$