Question

How do you solve `-20x^2 - 20x + 40 = 0`?

Answer 1

You may start by dividing everything by `20`
It also helps if you reverse all the signs.

Explanation:

`->-x^2-x+2=0`
`->x^2+x-2=0`

This can be factorised:
`->(x-1)*(x+2)=0`
`->x=1orx=-2`

Answer 2

I found:
`x_1-=1`
`x_2=-2`

Explanation:

Again, you can use the Quadratic Formula but we can also try something...interesting!
Divide all by `20`;
`-x^2-x+2=0`
Rearrange:
`-x^2-x=-2`
again...
`x^2+x=2`
add and subtract `1/4`;
`x^2+x+1/4-1/4=2`
rearrange:
`x^2+x+1/4=2+1/4`
`(x+1/2)^2=9/4`
root square both sides:
`x+1/2=+-sqrt(9/4)=+-3/2`
so you get two solutions:
`x_1=-1/2+3/2=1`
`x_2=-1/2-3/2=-2`