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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+4x^2-24x+3x-18)=0

We get rid of parentheses

4x^2-24x+3x-18=0

We add all the numbers together, and all the variables

4x^2-21x-18=0

a = 4; b = -21; c = -18;
Δ = b2-4ac
Δ = -212-4·4·(-18)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-27}{2*4}=\frac{-6}{8}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+27}{2*4}=\frac{48}{8}
=6
$