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 ..

(+2x^2-6x+8x-24)+x-50=0

We get rid of parentheses

2x^2-6x+8x+x-24-50=0

We add all the numbers together, and all the variables

2x^2+3x-74=0

a = 2; b = 3; c = -74;
Δ = b2-4ac
Δ = 32-4·2·(-74)
Δ = 601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{601}}{2*2}=\frac{-3-\sqrt{601}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{601}}{2*2}=\frac{-3+\sqrt{601}}{4}
$