-5=5/2m-m

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

-5=5/2m-m

We move all terms to the left:

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


Domain of the equation: 2m-m)!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1m-5/2m-5=0

We multiply all the terms by the denominator


1m*2m-5*2m-5=0

Wy multiply elements

2m^2-10m-5=0

a = 2; b = -10; c = -5;
Δ = b2-4ac
Δ = -102-4·2·(-5)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{35}}{2*2}=\frac{10-2\sqrt{35}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{35}}{2*2}=\frac{10+2\sqrt{35}}{4}
$