(2x+8)(4x-14)=42

Solution for (2x+8)(4x-14)=42 equation:

(2x+8)(4x-14)=42

We move all terms to the left:

(2x+8)(4x-14)-(42)=0

We multiply parentheses ..

(+8x^2-28x+32x-112)-42=0

We get rid of parentheses

8x^2-28x+32x-112-42=0

We add all the numbers together, and all the variables

8x^2+4x-154=0

a = 8; b = 4; c = -154;
Δ = b2-4ac
Δ = 42-4·8·(-154)
Δ = 4944
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:

$\sqrt{\Delta}=\sqrt{4944}=\sqrt{16*309}=\sqrt{16}*\sqrt{309}=4\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{309}}{2*8}=\frac{-4-4\sqrt{309}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{309}}{2*8}=\frac{-4+4\sqrt{309}}{16}
$