How do I solve this equation?

-1.6x^2 - 3.2x + 18 = 0
-16x^2 - 32x + 180 = 0
-4x^2 - 8x + 45 = 0
(-2x + 5)(2x + 9) = 0

-2x + 5 = 0
-2x = -5
x = -5/-2
x = 5/2 (2.5)

2x + 9 = 0
2x = -9
x = -9/2 (-4.5)

∴ x = 5/2 (2.5) , -9/2 (-4.5)

16x² + 32x - 180 = 0
4x² + 8x - 45 = 0
(2x + 9)(2x - 5) = 0
x = - 4.5 , x = 2.5

start with
x^2+2x-(18/1.6)=0
with the solutions
x(1)=-1+sqrt[1+(18/1.6)]
x(2)=-1-sqrt[1+(18/1.6)]

Use the quadratic formula noting that

a = -1.6
b = -3.2
c = 18

and your roots will be

x = -4.5 and x = 2.5

divide by -1.6

x^2 + 2x - 18/1.6 = 0

x^2 + 2x - 45/4 = 0

(x - 5/2)(x + 9/2) = 0

x = 5/2, -9/2

-1.6x^2 - 3.2x + 18 = 0

x^2 + 2x - 11.25 = 0
(x-2.5)(x+4.5) = 0
x = 2.5, -4.5

I'd multiply everything by -10 to get rid of the decimals.

16x^2 + 32x - 180 = 0. Divide everything by 4.

4x^2 + 8x - 45 = 0. Having it this way instead of the original way makes it MUCH easier to factor.

(2x - 5)(2x + 9) = 0.

x = 5/2 and x = -9/2.

-John

Use the equation x=(-b+||-sqrt(b^2-4ac))/a

from this model of your current equation where a b and c are the coefficients and constants

ax^2+bx+c=0

when you to the answers you should get 2.5 and -4.5

if you want to factor that it's (x+4.5)(x-2.5)=0