(4x-5)(3-6x)=0

Solution for (4x-5)(3-6x)=0 equation:

(4x-5)(3-6x)=0

We add all the numbers together, and all the variables

(4x-5)(-6x+3)=0

We multiply parentheses ..

(-24x^2+12x+30x-15)=0

We get rid of parentheses

-24x^2+12x+30x-15=0

We add all the numbers together, and all the variables

-24x^2+42x-15=0

a = -24; b = 42; c = -15;
Δ = b2-4ac
Δ = 422-4·(-24)·(-15)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-18}{2*-24}=\frac{-60}{-48}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+18}{2*-24}=\frac{-24}{-48}
=1/2
$