1-2m-5m2=0

Solution for 1-2m-5m2=0 equation:

1-2m-5m^2=0

a = -5; b = -2; c = +1;
Δ = b2-4ac
Δ = -22-4·(-5)·1
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{6}}{2*-5}=\frac{2-2\sqrt{6}}{-10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{6}}{2*-5}=\frac{2+2\sqrt{6}}{-10}
$