5(1+2m)=(1/2)(8+20m)

Solution for 5(1+2m)=(1/2)(8+20m) equation:

5(1+2m)=(1/2)(8+20m)

We move all terms to the left:

5(1+2m)-((1/2)(8+20m))=0


Domain of the equation: 2)(8+20m))!=0

m∈R


We add all the numbers together, and all the variables

5(2m+1)-((+1/2)(20m+8))=0

We multiply parentheses

10m-((+1/2)(20m+8))+5=0

We multiply parentheses ..

-((+20m^2+1/2*8))+10m+5=0

We multiply all the terms by the denominator


-((+20m^2+1+10m*2*8))+5*2*8))=0


We calculate terms in parentheses: -((+20m^2+1+10m*2*8)), so:

(+20m^2+1+10m*2*8)

We get rid of parentheses

20m^2+10m*2*8+1

Wy multiply elements

20m^2+160m*8+1

Wy multiply elements

20m^2+1280m+1

Back to the equation:

-(20m^2+1280m+1)


We add all the numbers together, and all the variables

-(20m^2+1280m+1)=0

We get rid of parentheses

-20m^2-1280m-1=0

a = -20; b = -1280; c = -1;
Δ = b2-4ac
Δ = -12802-4·(-20)·(-1)
Δ = 1638320
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:

$\sqrt{\Delta}=\sqrt{1638320}=\sqrt{16*102395}=\sqrt{16}*\sqrt{102395}=4\sqrt{102395}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1280)-4\sqrt{102395}}{2*-20}=\frac{1280-4\sqrt{102395}}{-40}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1280)+4\sqrt{102395}}{2*-20}=\frac{1280+4\sqrt{102395}}{-40}
$