X*(2x+1)=120

Solution for X*(2x+1)=120 equation:

X*(2X+1)=120

We move all terms to the left:

X*(2X+1)-(120)=0

We multiply parentheses

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
$