(2,5x-5)(x-9)=0

Solution for (2,5x-5)(x-9)=0 equation:

(2.5x-5)(x-9)=0

We multiply parentheses ..

(+2x^2-18x-5x+45)=0

We get rid of parentheses

2x^2-18x-5x+45=0

We add all the numbers together, and all the variables

2x^2-23x+45=0

a = 2; b = -23; c = +45;
Δ = b2-4ac
Δ = -232-4·2·45
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-13}{2*2}=\frac{10}{4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+13}{2*2}=\frac{36}{4}
=9
$