4m^2-5=-10m

Solution for 4m^2-5=-10m equation:

4m^2-5=-10m

We move all terms to the left:

4m^2-5-(-10m)=0

We get rid of parentheses

4m^2+10m-5=0

a = 4; b = 10; c = -5;
Δ = b2-4ac
Δ = 102-4·4·(-5)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{5}}{2*4}=\frac{-10-6\sqrt{5}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{5}}{2*4}=\frac{-10+6\sqrt{5}}{8}
$