(5x-9)(x+0.5)=0

Solution for (5x-9)(x+0.5)=0 equation:

(5x-9)(x+0.5)=0

We multiply parentheses ..

(+5x^2+2.5x-9x-4.5)=0

We get rid of parentheses

5x^2+2.5x-9x-4.5=0

We add all the numbers together, and all the variables

5x^2-6.5x-4.5=0

a = 5; b = -6.5; c = -4.5;
Δ = b2-4ac
Δ = -6.52-4·5·(-4.5)
Δ = 132.25
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{-(-6.5)-\sqrt{132.25}}{2*5}=\frac{6.5-\sqrt{132.25}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6.5)+\sqrt{132.25}}{2*5}=\frac{6.5+\sqrt{132.25}}{10}
$