8x^2-2x-186=0

Solution for 8x^2-2x-186=0 equation:

8x^2-2x-186=0

a = 8; b = -2; c = -186;
Δ = b2-4ac
Δ = -22-4·8·(-186)
Δ = 5956
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5956}=\sqrt{4*1489}=\sqrt{4}*\sqrt{1489}=2\sqrt{1489}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{1489}}{2*8}=\frac{2-2\sqrt{1489}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{1489}}{2*8}=\frac{2+2\sqrt{1489}}{16}
$