2(x+1)(x-7)=54

Solution for 2(x+1)(x-7)=54 equation:

2(x+1)(x-7)=54

We move all terms to the left:

2(x+1)(x-7)-(54)=0

We multiply parentheses ..

2(+x^2-7x+x-7)-54=0

We multiply parentheses

2x^2-14x+2x-14-54=0

We add all the numbers together, and all the variables

2x^2-12x-68=0

a = 2; b = -12; c = -68;
Δ = b2-4ac
Δ = -122-4·2·(-68)
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{43}}{2*2}=\frac{12-4\sqrt{43}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{43}}{2*2}=\frac{12+4\sqrt{43}}{4}
$