120=(2x-1)(x)

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

120=(2x-1)(x)

We move all terms to the left:

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


We calculate terms in parentheses: -((2x-1)x), so:

(2x-1)x

We multiply parentheses

2x^2-1x

Back to the equation:

-(2x^2-1x)


We get rid of parentheses

-2x^2+1x+120=0

We add all the numbers together, and all the variables

-2x^2+x+120=0

a = -2; b = 1; c = +120;
Δ = b2-4ac
Δ = 12-4·(-2)·120
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-31}{2*-2}=\frac{-32}{-4}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+31}{2*-2}=\frac{30}{-4}
=-7+1/2
$