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

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

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

We move all terms to the left:

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


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

m∈R


We add all the numbers together, and all the variables

5(2m+1)-(1/228m)=0

We multiply parentheses

10m-(1/228m)+5=0

We get rid of parentheses

10m-1/228m+5=0

We multiply all the terms by the denominator


10m*228m+5*228m-1=0

Wy multiply elements

2280m^2+1140m-1=0

a = 2280; b = 1140; c = -1;
Δ = b2-4ac
Δ = 11402-4·2280·(-1)
Δ = 1308720
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:

$\sqrt{\Delta}=\sqrt{1308720}=\sqrt{16*81795}=\sqrt{16}*\sqrt{81795}=4\sqrt{81795}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1140)-4\sqrt{81795}}{2*2280}=\frac{-1140-4\sqrt{81795}}{4560}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1140)+4\sqrt{81795}}{2*2280}=\frac{-1140+4\sqrt{81795}}{4560}
$