38=(x-120)(2x+1)

Solution for 38=(x-120)(2x+1) equation:

38=(x-120)(2x+1)

We move all terms to the left:

38-((x-120)(2x+1))=0

We multiply parentheses ..

-((+2x^2+x-240x-120))+38=0


We calculate terms in parentheses: -((+2x^2+x-240x-120)), so:

(+2x^2+x-240x-120)

We get rid of parentheses

2x^2+x-240x-120

We add all the numbers together, and all the variables

2x^2-239x-120

Back to the equation:

-(2x^2-239x-120)


We get rid of parentheses

-2x^2+239x+120+38=0

We add all the numbers together, and all the variables

-2x^2+239x+158=0

a = -2; b = 239; c = +158;
Δ = b2-4ac
Δ = 2392-4·(-2)·158
Δ = 58385
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{-(239)-\sqrt{58385}}{2*-2}=\frac{-239-\sqrt{58385}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(239)+\sqrt{58385}}{2*-2}=\frac{-239+\sqrt{58385}}{-4}
$