x(x+4)+(2x-6)=50

Solution for x(x+4)+(2x-6)=50 equation:

x(x+4)+(2x-6)=50

We move all terms to the left:

x(x+4)+(2x-6)-(50)=0

We multiply parentheses

x^2+4x+(2x-6)-50=0

We get rid of parentheses

x^2+4x+2x-6-50=0

We add all the numbers together, and all the variables

x^2+6x-56=0

a = 1; b = 6; c = -56;
Δ = b2-4ac
Δ = 62-4·1·(-56)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{65}}{2*1}=\frac{-6-2\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{65}}{2*1}=\frac{-6+2\sqrt{65}}{2}
$