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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

42x^2-9x-6=0

a = 42; b = -9; c = -6;
Δ = b2-4ac
Δ = -92-4·42·(-6)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-33}{2*42}=\frac{-24}{84}
=-2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+33}{2*42}=\frac{42}{84}
=1/2
$