5/2m=2m+5

Solution for 5/2m=2m+5 equation:

5/2m=2m+5

We move all terms to the left:

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


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We get rid of parentheses

5/2m-2m-5=0

We multiply all the terms by the denominator


-2m*2m-5*2m+5=0

Wy multiply elements

-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}
$