6y^2-7y-55=0

Solution for 6y^2-7y-55=0 equation:

6y^2-7y-55=0

a = 6; b = -7; c = -55;
Δ = b2-4ac
Δ = -72-4·6·(-55)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-37}{2*6}=\frac{-30}{12}
=-2+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+37}{2*6}=\frac{44}{12}
=3+2/3
$