(6x-1)(7x+4)=0

Solution for (6x-1)(7x+4)=0 equation:

(6x-1)(7x+4)=0

We multiply parentheses ..

(+42x^2+24x-7x-4)=0

We get rid of parentheses

42x^2+24x-7x-4=0

We add all the numbers together, and all the variables

42x^2+17x-4=0

a = 42; b = 17; c = -4;
Δ = b2-4ac
Δ = 172-4·42·(-4)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-31}{2*42}=\frac{-48}{84}
=-4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+31}{2*42}=\frac{14}{84}
=1/6
$