6r^2-13r-63=0

Solution for 6r^2-13r-63=0 equation:

6r^2-13r-63=0

a = 6; b = -13; c = -63;
Δ = b2-4ac
Δ = -132-4·6·(-63)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-41}{2*6}=\frac{-28}{12}
=-2+1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+41}{2*6}=\frac{54}{12}
=4+1/2
$