1/2m-5+2m=20

Solution for 1/2m-5+2m=20 equation:

1/2m-5+2m=20

We move all terms to the left:

1/2m-5+2m-(20)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

2m+1/2m-25=0

We multiply all the terms by the denominator


2m*2m-25*2m+1=0

Wy multiply elements

4m^2-50m+1=0

a = 4; b = -50; c = +1;
Δ = b2-4ac
Δ = -502-4·4·1
Δ = 2484
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:

$\sqrt{\Delta}=\sqrt{2484}=\sqrt{36*69}=\sqrt{36}*\sqrt{69}=6\sqrt{69}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-6\sqrt{69}}{2*4}=\frac{50-6\sqrt{69}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+6\sqrt{69}}{2*4}=\frac{50+6\sqrt{69}}{8}
$