5y^2+44y+46=0

Solution for 5y^2+44y+46=0 equation:

5y^2+44y+46=0

a = 5; b = 44; c = +46;
Δ = b2-4ac
Δ = 442-4·5·46
Δ = 1016
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:

$\sqrt{\Delta}=\sqrt{1016}=\sqrt{4*254}=\sqrt{4}*\sqrt{254}=2\sqrt{254}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-2\sqrt{254}}{2*5}=\frac{-44-2\sqrt{254}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+2\sqrt{254}}{2*5}=\frac{-44+2\sqrt{254}}{10}
$