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

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

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

We add all the numbers together, and all the variables

(-5x+9)(-1x+5)=0

We multiply parentheses ..

(+5x^2-25x-9x+45)=0

We get rid of parentheses

5x^2-25x-9x+45=0

We add all the numbers together, and all the variables

5x^2-34x+45=0

a = 5; b = -34; c = +45;
Δ = b2-4ac
Δ = -342-4·5·45
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-16}{2*5}=\frac{18}{10}
=1+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+16}{2*5}=\frac{50}{10}
=5
$