-1/2m^2+5=-10

Solution for -1/2m^2+5=-10 equation:

-1/2m^2+5=-10

We move all terms to the left:

-1/2m^2+5-(-10)=0


Domain of the equation: 2m^2!=0

m^2!=0/2

m^2!=√0

m!=0

m∈R


We add all the numbers together, and all the variables

-1/2m^2+15=0

We multiply all the terms by the denominator


15*2m^2-1=0

Wy multiply elements

30m^2-1=0

a = 30; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·30·(-1)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*30}=\frac{0-2\sqrt{30}}{60}
=-\frac{2\sqrt{30}}{60}
=-\frac{\sqrt{30}}{30}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*30}=\frac{0+2\sqrt{30}}{60}
=\frac{2\sqrt{30}}{60}
=\frac{\sqrt{30}}{30}
$