(2x-7)(6x+3)=0

Solution for (2x-7)(6x+3)=0 equation:

(2x-7)(6x+3)=0

We multiply parentheses ..

(+12x^2+6x-42x-21)=0

We get rid of parentheses

12x^2+6x-42x-21=0

We add all the numbers together, and all the variables

12x^2-36x-21=0

a = 12; b = -36; c = -21;
Δ = b2-4ac
Δ = -362-4·12·(-21)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-48}{2*12}=\frac{-12}{24}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+48}{2*12}=\frac{84}{24}
=3+1/2
$