1/2m+4m=3m-5

Solution for 1/2m+4m=3m-5 equation:

1/2m+4m=3m-5

We move all terms to the left:

1/2m+4m-(3m-5)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

4m+1/2m-(3m-5)=0

We get rid of parentheses

4m+1/2m-3m+5=0

We multiply all the terms by the denominator


4m*2m-3m*2m+5*2m+1=0

Wy multiply elements

8m^2-6m^2+10m+1=0

We add all the numbers together, and all the variables

2m^2+10m+1=0

a = 2; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·2·1
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{23}}{2*2}=\frac{-10-2\sqrt{23}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{23}}{2*2}=\frac{-10+2\sqrt{23}}{4}
$