3y^2-4y-75=0

Solution for 3y^2-4y-75=0 equation:

3y^2-4y-75=0

a = 3; b = -4; c = -75;
Δ = b2-4ac
Δ = -42-4·3·(-75)
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{229}}{2*3}=\frac{4-2\sqrt{229}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{229}}{2*3}=\frac{4+2\sqrt{229}}{6}
$