9/5m+8=2m

Solution for 9/5m+8=2m equation:

9/5m+8=2m

We move all terms to the left:

9/5m+8-(2m)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R


We add all the numbers together, and all the variables

-2m+9/5m+8=0

We multiply all the terms by the denominator


-2m*5m+8*5m+9=0

Wy multiply elements

-10m^2+40m+9=0

a = -10; b = 40; c = +9;
Δ = b2-4ac
Δ = 402-4·(-10)·9
Δ = 1960
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:

$\sqrt{\Delta}=\sqrt{1960}=\sqrt{196*10}=\sqrt{196}*\sqrt{10}=14\sqrt{10}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-14\sqrt{10}}{2*-10}=\frac{-40-14\sqrt{10}}{-20}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+14\sqrt{10}}{2*-10}=\frac{-40+14\sqrt{10}}{-20}
$