7r2-6r-7=0

Solution for 7r2-6r-7=0 equation:

7r^2-6r-7=0

a = 7; b = -6; c = -7;
Δ = b2-4ac
Δ = -62-4·7·(-7)
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{58}}{2*7}=\frac{6-2\sqrt{58}}{14}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{58}}{2*7}=\frac{6+2\sqrt{58}}{14}
$