4x^2+16x=-14

Solution for 4x^2+16x=-14 equation:

4x^2+16x=-14

We move all terms to the left:

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

We add all the numbers together, and all the variables

4x^2+16x+14=0

a = 4; b = 16; c = +14;
Δ = b2-4ac
Δ = 162-4·4·14
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{2}}{2*4}=\frac{-16-4\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{2}}{2*4}=\frac{-16+4\sqrt{2}}{8}
$