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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-24x^2+12x-18x+9)=0

We get rid of parentheses

-24x^2+12x-18x+9=0

We add all the numbers together, and all the variables

-24x^2-6x+9=0

a = -24; b = -6; c = +9;
Δ = b2-4ac
Δ = -62-4·(-24)·9
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-30}{2*-24}=\frac{-24}{-48}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30}{2*-24}=\frac{36}{-48}
=-3/4
$