(x+5)(x-49)=52

Solution for (x+5)(x-49)=52 equation:

(x+5)(x-49)=52

We move all terms to the left:

(x+5)(x-49)-(52)=0

We multiply parentheses ..

(+x^2-49x+5x-245)-52=0

We get rid of parentheses

x^2-49x+5x-245-52=0

We add all the numbers together, and all the variables

x^2-44x-297=0

a = 1; b = -44; c = -297;
Δ = b2-4ac
Δ = -442-4·1·(-297)
Δ = 3124
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:

$\sqrt{\Delta}=\sqrt{3124}=\sqrt{4*781}=\sqrt{4}*\sqrt{781}=2\sqrt{781}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{781}}{2*1}=\frac{44-2\sqrt{781}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{781}}{2*1}=\frac{44+2\sqrt{781}}{2}
$