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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

7x^2-38x-24=0

a = 7; b = -38; c = -24;
Δ = b2-4ac
Δ = -382-4·7·(-24)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-46}{2*7}=\frac{-8}{14}
=-4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+46}{2*7}=\frac{84}{14}
=6
$