3x(x+2)-4x(x+6)=77

Solution for 3x(x+2)-4x(x+6)=77 equation:

3x(x+2)-4x(x+6)=77

We move all terms to the left:

3x(x+2)-4x(x+6)-(77)=0

We multiply parentheses

3x^2-4x^2+6x-24x-77=0

We add all the numbers together, and all the variables

-1x^2-18x-77=0

a = -1; b = -18; c = -77;
Δ = b2-4ac
Δ = -182-4·(-1)·(-77)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4}{2*-1}=\frac{14}{-2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4}{2*-1}=\frac{22}{-2}
=-11
$