2m=7/5m+5

Solution for 2m=7/5m+5 equation:

2m=7/5m+5

We move all terms to the left:

2m-(7/5m+5)=0


Domain of the equation: 5m+5)!=0

m∈R


We get rid of parentheses

2m-7/5m-5=0

We multiply all the terms by the denominator


2m*5m-5*5m-7=0

Wy multiply elements

10m^2-25m-7=0

a = 10; b = -25; c = -7;
Δ = b2-4ac
Δ = -252-4·10·(-7)
Δ = 905
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-\sqrt{905}}{2*10}=\frac{25-\sqrt{905}}{20}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{905}}{2*10}=\frac{25+\sqrt{905}}{20}
$