0=16x^2+8x-7

Solution for 0=16x^2+8x-7 equation:

0=16x^2+8x-7

We move all terms to the left:

0-(16x^2+8x-7)=0

We add all the numbers together, and all the variables

-(16x^2+8x-7)=0

We get rid of parentheses

-16x^2-8x+7=0

a = -16; b = -8; c = +7;
Δ = b2-4ac
Δ = -82-4·(-16)·7
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16\sqrt{2}}{2*-16}=\frac{8-16\sqrt{2}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16\sqrt{2}}{2*-16}=\frac{8+16\sqrt{2}}{-32}
$