(2x-19)(2x-32)=264

Solution for (2x-19)(2x-32)=264 equation:

(2x-19)(2x-32)=264

We move all terms to the left:

(2x-19)(2x-32)-(264)=0

We multiply parentheses ..

(+4x^2-64x-38x+608)-264=0

We get rid of parentheses

4x^2-64x-38x+608-264=0

We add all the numbers together, and all the variables

4x^2-102x+344=0

a = 4; b = -102; c = +344;
Δ = b2-4ac
Δ = -1022-4·4·344
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-70}{2*4}=\frac{32}{8}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+70}{2*4}=\frac{172}{8}
=21+1/2
$