(4x+3)(2x-6)=0

Solution for (4x+3)(2x-6)=0 equation:

(4x+3)(2x-6)=0

We multiply parentheses ..

(+8x^2-24x+6x-18)=0

We get rid of parentheses

8x^2-24x+6x-18=0

We add all the numbers together, and all the variables

8x^2-18x-18=0

a = 8; b = -18; c = -18;
Δ = b2-4ac
Δ = -182-4·8·(-18)
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{-(-18)-30}{2*8}=\frac{-12}{16}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+30}{2*8}=\frac{48}{16}
=3
$