4x(2x+7)-16=-14

Solution for 4x(2x+7)-16=-14 equation:

4x(2x+7)-16=-14

We move all terms to the left:

4x(2x+7)-16-(-14)=0

We add all the numbers together, and all the variables

4x(2x+7)-2=0

We multiply parentheses

8x^2+28x-2=0

a = 8; b = 28; c = -2;
Δ = b2-4ac
Δ = 282-4·8·(-2)
Δ = 848
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:

$\sqrt{\Delta}=\sqrt{848}=\sqrt{16*53}=\sqrt{16}*\sqrt{53}=4\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{53}}{2*8}=\frac{-28-4\sqrt{53}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{53}}{2*8}=\frac{-28+4\sqrt{53}}{16}
$