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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

7a^2+38a-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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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