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

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

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

We multiply parentheses ..

(+42x^2-18x+14x-6)=0

We get rid of parentheses

42x^2-18x+14x-6=0

We add all the numbers together, and all the variables

42x^2-4x-6=0

a = 42; b = -4; c = -6;
Δ = b2-4ac
Δ = -42-4·42·(-6)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-32}{2*42}=\frac{-28}{84}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+32}{2*42}=\frac{36}{84}
=3/7
$