19y^2+2y-45=0

Solution for 19y^2+2y-45=0 equation:

19y^2+2y-45=0

a = 19; b = 2; c = -45;
Δ = b2-4ac
Δ = 22-4·19·(-45)
Δ = 3424
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:

$\sqrt{\Delta}=\sqrt{3424}=\sqrt{16*214}=\sqrt{16}*\sqrt{214}=4\sqrt{214}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{214}}{2*19}=\frac{-2-4\sqrt{214}}{38}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{214}}{2*19}=\frac{-2+4\sqrt{214}}{38}
$