29y^2-42y-11=0

Solution for 29y^2-42y-11=0 equation:

29y^2-42y-11=0

a = 29; b = -42; c = -11;
Δ = b2-4ac
Δ = -422-4·29·(-11)
Δ = 3040
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:

$\sqrt{\Delta}=\sqrt{3040}=\sqrt{16*190}=\sqrt{16}*\sqrt{190}=4\sqrt{190}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-4\sqrt{190}}{2*29}=\frac{42-4\sqrt{190}}{58}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+4\sqrt{190}}{2*29}=\frac{42+4\sqrt{190}}{58}
$