(x+4)(x+8)=50

Solution for (x+4)(x+8)=50 equation:

(x+4)(x+8)=50

We move all terms to the left:

(x+4)(x+8)-(50)=0

We multiply parentheses ..

(+x^2+8x+4x+32)-50=0

We get rid of parentheses

x^2+8x+4x+32-50=0

We add all the numbers together, and all the variables

x^2+12x-18=0

a = 1; b = 12; c = -18;
Δ = b2-4ac
Δ = 122-4·1·(-18)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{6}}{2*1}=\frac{-12-6\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{6}}{2*1}=\frac{-12+6\sqrt{6}}{2}
$