2m2+5=10m

Solution for 2m2+5=10m equation:

2m^2+5=10m

We move all terms to the left:

2m^2+5-(10m)=0

a = 2; b = -10; c = +5;
Δ = b2-4ac
Δ = -102-4·2·5
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{15}}{2*2}=\frac{10-2\sqrt{15}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{15}}{2*2}=\frac{10+2\sqrt{15}}{4}
$