10m^2-5=-5m

Solution for 10m^2-5=-5m equation:

10m^2-5=-5m

We move all terms to the left:

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

We get rid of parentheses

10m^2+5m-5=0

a = 10; b = 5; c = -5;
Δ = b2-4ac
Δ = 52-4·10·(-5)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-15}{2*10}=\frac{-20}{20}
=-1
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+15}{2*10}=\frac{10}{20}
=1/2
$