y^2-4y-186=0

Solution for y^2-4y-186=0 equation:

y^2-4y-186=0

a = 1; b = -4; c = -186;
Δ = b2-4ac
Δ = -42-4·1·(-186)
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{190}}{2*1}=\frac{4-2\sqrt{190}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{190}}{2*1}=\frac{4+2\sqrt{190}}{2}
$