.5(2x+14)(x+2)=50

Solution for .5(2x+14)(x+2)=50 equation:

.5(2x+14)(x+2)=50

We move all terms to the left:

.5(2x+14)(x+2)-(50)=0

We multiply parentheses ..

.5(+2x^2+4x+14x+28)-50=0

We multiply parentheses

x^2+2x+7x+14-50=0

We add all the numbers together, and all the variables

x^2+9x-36=0

a = 1; b = 9; c = -36;
Δ = b2-4ac
Δ = 92-4·1·(-36)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-15}{2*1}=\frac{-24}{2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+15}{2*1}=\frac{6}{2}
=3
$