3y^2-10y-81=0

Solution for 3y^2-10y-81=0 equation:

3y^2-10y-81=0

a = 3; b = -10; c = -81;
Δ = b2-4ac
Δ = -102-4·3·(-81)
Δ = 1072
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{67}}{2*3}=\frac{10-4\sqrt{67}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{67}}{2*3}=\frac{10+4\sqrt{67}}{6}
$