-16x+7+4x^2=-7

Solution for -16x+7+4x^2=-7 equation:

-16x+7+4x^2=-7

We move all terms to the left:

-16x+7+4x^2-(-7)=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}
$