11y^2-24y-4=0

Solution for 11y^2-24y-4=0 equation:

11y^2-24y-4=0

a = 11; b = -24; c = -4;
Δ = b2-4ac
Δ = -242-4·11·(-4)
Δ = 752
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:

$\sqrt{\Delta}=\sqrt{752}=\sqrt{16*47}=\sqrt{16}*\sqrt{47}=4\sqrt{47}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{47}}{2*11}=\frac{24-4\sqrt{47}}{22}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{47}}{2*11}=\frac{24+4\sqrt{47}}{22}
$