12r2-13r-35=0

Solution for 12r2-13r-35=0 equation:

12r^2-13r-35=0

a = 12; b = -13; c = -35;
Δ = b2-4ac
Δ = -132-4·12·(-35)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-43}{2*12}=\frac{-30}{24}
=-1+1/4
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+43}{2*12}=\frac{56}{24}
=2+1/3
$