(x+6)(6x-8)=0

Solution for (x+6)(6x-8)=0 equation:

(x+6)(6x-8)=0

We multiply parentheses ..

(+6x^2-8x+36x-48)=0

We get rid of parentheses

6x^2-8x+36x-48=0

We add all the numbers together, and all the variables

6x^2+28x-48=0

a = 6; b = 28; c = -48;
Δ = b2-4ac
Δ = 282-4·6·(-48)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-44}{2*6}=\frac{-72}{12}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+44}{2*6}=\frac{16}{12}
=1+1/3
$