(50-2x)(39-2x)=574

Solution for (50-2x)(39-2x)=574 equation:

(50-2x)(39-2x)=574

We move all terms to the left:

(50-2x)(39-2x)-(574)=0

We add all the numbers together, and all the variables

(-2x+50)(-2x+39)-574=0

We multiply parentheses ..

(+4x^2-78x-100x+1950)-574=0

We get rid of parentheses

4x^2-78x-100x+1950-574=0

We add all the numbers together, and all the variables

4x^2-178x+1376=0

a = 4; b = -178; c = +1376;
Δ = b2-4ac
Δ = -1782-4·4·1376
Δ = 9668
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9668}=\sqrt{4*2417}=\sqrt{4}*\sqrt{2417}=2\sqrt{2417}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-178)-2\sqrt{2417}}{2*4}=\frac{178-2\sqrt{2417}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-178)+2\sqrt{2417}}{2*4}=\frac{178+2\sqrt{2417}}{8}
$