7r^2-8r-7=0

Solution for 7r^2-8r-7=0 equation:

7r^2-8r-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:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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