(19-2x)(35-2x)=561

Solution for (19-2x)(35-2x)=561 equation:

(19-2x)(35-2x)=561

We move all terms to the left:

(19-2x)(35-2x)-(561)=0

We add all the numbers together, and all the variables

(-2x+19)(-2x+35)-561=0

We multiply parentheses ..

(+4x^2-70x-38x+665)-561=0

We get rid of parentheses

4x^2-70x-38x+665-561=0

We add all the numbers together, and all the variables

4x^2-108x+104=0

a = 4; b = -108; c = +104;
Δ = b2-4ac
Δ = -1082-4·4·104
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-100}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+100}{2*4}=\frac{208}{8}
=26
$