-00.5(x^2-26x-120)=0

Solution for -00.5(x^2-26x-120)=0 equation:

-00.5(x^2-26x-120)=0

We multiply parentheses

-0.5x^2+13x+60=0

a = -0.5; b = 13; c = +60;
Δ = b2-4ac
Δ = 132-4·(-0.5)·60
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-17}{2*-0.5}=\frac{-30}{-1}
=+30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+17}{2*-0.5}=\frac{4}{-1}
=-4
$