0=((-5x^2)-10x+120)

Solution for 0=((-5x^2)-10x+120) equation:

0=((-5x^2)-10x+120)

We move all terms to the left:

0-(((-5x^2)-10x+120))=0

We add all the numbers together, and all the variables

-(((-5x^2)-10x+120))=0


We calculate terms in parentheses: -(((-5x^2)-10x+120)), so:

((-5x^2)-10x+120)


We calculate terms in parentheses: +((-5x^2)-10x+120), so:

(-5x^2)-10x+120

We get rid of parentheses

-5x^2-10x+120

Back to the equation:

+(-5x^2-10x+120)


We get rid of parentheses

-5x^2-10x+120

Back to the equation:

-(-5x^2-10x+120)


We get rid of parentheses

5x^2+10x-120=0

a = 5; b = 10; c = -120;
Δ = b2-4ac
Δ = 102-4·5·(-120)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-50}{2*5}=\frac{-60}{10}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+50}{2*5}=\frac{40}{10}
=4
$