0=4x^2+8x-7

Solution for 0=4x^2+8x-7 equation:

0=4x^2+8x-7

We move all terms to the left:

0-(4x^2+8x-7)=0

We add all the numbers together, and all the variables

-(4x^2+8x-7)=0

We get rid of parentheses

-4x^2-8x+7=0

a = -4; b = -8; c = +7;
Δ = b2-4ac
Δ = -82-4·(-4)·7
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{11}}{2*-4}=\frac{8-4\sqrt{11}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{11}}{2*-4}=\frac{8+4\sqrt{11}}{-8}
$