(4x-2)(9-15x)=0

Solution for (4x-2)(9-15x)=0 equation:

(4x-2)(9-15x)=0

We add all the numbers together, and all the variables

(4x-2)(-15x+9)=0

We multiply parentheses ..

(-60x^2+36x+30x-18)=0

We get rid of parentheses

-60x^2+36x+30x-18=0

We add all the numbers together, and all the variables

-60x^2+66x-18=0

a = -60; b = 66; c = -18;
Δ = b2-4ac
Δ = 662-4·(-60)·(-18)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-6}{2*-60}=\frac{-72}{-120}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+6}{2*-60}=\frac{-60}{-120}
=1/2
$