x(2x-5)=120

Solution for x(2x-5)=120 equation:

x(2x-5)=120

We move all terms to the left:

x(2x-5)-(120)=0

We multiply parentheses

2x^2-5x-120=0

a = 2; b = -5; c = -120;
Δ = b2-4ac
Δ = -52-4·2·(-120)
Δ = 985
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{-(-5)-\sqrt{985}}{2*2}=\frac{5-\sqrt{985}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{985}}{2*2}=\frac{5+\sqrt{985}}{4}
$