5y^2-4y-461=0

Solution for 5y^2-4y-461=0 equation:

5y^2-4y-461=0

a = 5; b = -4; c = -461;
Δ = b2-4ac
Δ = -42-4·5·(-461)
Δ = 9236
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:

$\sqrt{\Delta}=\sqrt{9236}=\sqrt{4*2309}=\sqrt{4}*\sqrt{2309}=2\sqrt{2309}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{2309}}{2*5}=\frac{4-2\sqrt{2309}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{2309}}{2*5}=\frac{4+2\sqrt{2309}}{10}
$