12y^2-13y-140=0

Solution for 12y^2-13y-140=0 equation:

12y^2-13y-140=0

a = 12; b = -13; c = -140;
Δ = b2-4ac
Δ = -132-4·12·(-140)
Δ = 6889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6889}=83$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-83}{2*12}=\frac{-70}{24}
=-2+11/12
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+83}{2*12}=\frac{96}{24}
=4
$