(x+3)(x+49)=360

Solution for (x+3)(x+49)=360 equation:

(x+3)(x+49)=360

We move all terms to the left:

(x+3)(x+49)-(360)=0

We multiply parentheses ..

(+x^2+49x+3x+147)-360=0

We get rid of parentheses

x^2+49x+3x+147-360=0

We add all the numbers together, and all the variables

x^2+52x-213=0

a = 1; b = 52; c = -213;
Δ = b2-4ac
Δ = 522-4·1·(-213)
Δ = 3556
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:

$\sqrt{\Delta}=\sqrt{3556}=\sqrt{4*889}=\sqrt{4}*\sqrt{889}=2\sqrt{889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-2\sqrt{889}}{2*1}=\frac{-52-2\sqrt{889}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+2\sqrt{889}}{2*1}=\frac{-52+2\sqrt{889}}{2}
$