0=8x+7-7x^2

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

0=8x+7-7x^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

7x^2-8x-7=0

a = 7; b = -8; c = -7;
Δ = b2-4ac
Δ = -82-4·7·(-7)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{65}}{2*7}=\frac{8-2\sqrt{65}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{65}}{2*7}=\frac{8+2\sqrt{65}}{14}
$