(x+38)(2x-6)+(x)=180

Solution for (x+38)(2x-6)+(x)=180 equation:

(x+38)(2x-6)+(x)=180

We move all terms to the left:

(x+38)(2x-6)+(x)-(180)=0

We add all the numbers together, and all the variables

x+(x+38)(2x-6)-180=0

We multiply parentheses ..

(+2x^2-6x+76x-228)+x-180=0

We get rid of parentheses

2x^2-6x+76x+x-228-180=0

We add all the numbers together, and all the variables

2x^2+71x-408=0

a = 2; b = 71; c = -408;
Δ = b2-4ac
Δ = 712-4·2·(-408)
Δ = 8305
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{-(71)-\sqrt{8305}}{2*2}=\frac{-71-\sqrt{8305}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(71)+\sqrt{8305}}{2*2}=\frac{-71+\sqrt{8305}}{4}
$