5x-4x(8x-9)=0

Solution for 5x-4x(8x-9)=0 equation:

5x-4x(8x-9)=0

We multiply parentheses

-32x^2+5x+36x=0

We add all the numbers together, and all the variables

-32x^2+41x=0

a = -32; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·(-32)·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*-32}=\frac{-82}{-64}
=1+9/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*-32}=\frac{0}{-64}
=0
$