m=4/5m+1

Solution for m=4/5m+1 equation:

m=4/5m+1

We move all terms to the left:

m-(4/5m+1)=0


Domain of the equation: 5m+1)!=0

m∈R


We get rid of parentheses

m-4/5m-1=0

We multiply all the terms by the denominator


m*5m-1*5m-4=0

Wy multiply elements

5m^2-5m-4=0

a = 5; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·5·(-4)
Δ = 105
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{-(-5)-\sqrt{105}}{2*5}=\frac{5-\sqrt{105}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{105}}{2*5}=\frac{5+\sqrt{105}}{10}
$