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

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

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

We multiply parentheses

-9x^2+5x+18x-10=0

We add all the numbers together, and all the variables

-9x^2+23x-10=0

a = -9; b = 23; c = -10;
Δ = b2-4ac
Δ = 232-4·(-9)·(-10)
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*-9}=\frac{-36}{-18}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+13}{2*-9}=\frac{-10}{-18}
=5/9
$