2x(7x+21)-8=54

Solution for 2x(7x+21)-8=54 equation:

2x(7x+21)-8=54

We move all terms to the left:

2x(7x+21)-8-(54)=0

We add all the numbers together, and all the variables

2x(7x+21)-62=0

We multiply parentheses

14x^2+42x-62=0

a = 14; b = 42; c = -62;
Δ = b2-4ac
Δ = 422-4·14·(-62)
Δ = 5236
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:

$\sqrt{\Delta}=\sqrt{5236}=\sqrt{4*1309}=\sqrt{4}*\sqrt{1309}=2\sqrt{1309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{1309}}{2*14}=\frac{-42-2\sqrt{1309}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{1309}}{2*14}=\frac{-42+2\sqrt{1309}}{28}
$