X(9-4x)-5=0

Solution for X(9-4x)-5=0 equation:

X(9-4X)-5=0

We add all the numbers together, and all the variables

X(-4X+9)-5=0

We multiply parentheses

-4X^2+9X-5=0

a = -4; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·(-4)·(-5)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-1}{2*-4}=\frac{-10}{-8}
=1+1/4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+1}{2*-4}=\frac{-8}{-8}
=1
$