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

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

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

We multiply parentheses ..

(+6x^2-42x+4x-28)=0

We get rid of parentheses

6x^2-42x+4x-28=0

We add all the numbers together, and all the variables

6x^2-38x-28=0

a = 6; b = -38; c = -28;
Δ = b2-4ac
Δ = -382-4·6·(-28)
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*6}=\frac{-8}{12}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+46}{2*6}=\frac{84}{12}
=7
$