7r^2-53r-117=0

Solution for 7r^2-53r-117=0 equation:

7r^2-53r-117=0

a = 7; b = -53; c = -117;
Δ = b2-4ac
Δ = -532-4·7·(-117)
Δ = 6085
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-\sqrt{6085}}{2*7}=\frac{53-\sqrt{6085}}{14}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+\sqrt{6085}}{2*7}=\frac{53+\sqrt{6085}}{14}
$