7(2x+6)3x+2=77

Solution for 7(2x+6)3x+2=77 equation:

7(2x+6)3x+2=77

We move all terms to the left:

7(2x+6)3x+2-(77)=0

We add all the numbers together, and all the variables

7(2x+6)3x-75=0

We multiply parentheses

42x^2+126x-75=0

a = 42; b = 126; c = -75;
Δ = b2-4ac
Δ = 1262-4·42·(-75)
Δ = 28476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28476}=\sqrt{36*791}=\sqrt{36}*\sqrt{791}=6\sqrt{791}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-6\sqrt{791}}{2*42}=\frac{-126-6\sqrt{791}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+6\sqrt{791}}{2*42}=\frac{-126+6\sqrt{791}}{84}
$