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

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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 $

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