14r^2-53r-14=0

Solution for 14r^2-53r-14=0 equation:

14r^2-53r-14=0

a = 14; b = -53; c = -14;
Δ = b2-4ac
Δ = -532-4·14·(-14)
Δ = 3593
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{3593}}{2*14}=\frac{53-\sqrt{3593}}{28}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+\sqrt{3593}}{2*14}=\frac{53+\sqrt{3593}}{28}
$