5(1+2m)=1/2(8+02m)

Solution for 5(1+2m)=1/2(8+02m) equation:

5(1+2m)=1/2(8+02m)

We move all terms to the left:

5(1+2m)-(1/2(8+02m))=0


Domain of the equation: 2(8+02m))!=0

m∈R


We add all the numbers together, and all the variables

5(2m+1)-(1/2(02m+8))=0

We multiply parentheses

10m-(1/2(02m+8))+5=0

We multiply all the terms by the denominator


10m*2(02m+8))-(1+5*2(02m+8))=0

Wy multiply elements

20m^2+10m=0

a = 20; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·20·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*20}=\frac{-20}{40}
=-1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*20}=\frac{0}{40}
=0
$