(4x-9)(-x+6)=0

Solution for (4x-9)(-x+6)=0 equation:

(4x-9)(-x+6)=0

We add all the numbers together, and all the variables

(4x-9)(-1x+6)=0

We multiply parentheses ..

(-4x^2+24x+9x-54)=0

We get rid of parentheses

-4x^2+24x+9x-54=0

We add all the numbers together, and all the variables

-4x^2+33x-54=0

a = -4; b = 33; c = -54;
Δ = b2-4ac
Δ = 332-4·(-4)·(-54)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-15}{2*-4}=\frac{-48}{-8}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+15}{2*-4}=\frac{-18}{-8}
=2+1/4
$