(10/m)+1=4m

Solution for (10/m)+1=4m equation:

(10/m)+1=4m

We move all terms to the left:

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


Domain of the equation: m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

(+10/m)-4m+1=0

We add all the numbers together, and all the variables

-4m+(+10/m)+1=0

We get rid of parentheses

-4m+10/m+1=0

We multiply all the terms by the denominator


-4m*m+1*m+10=0

We add all the numbers together, and all the variables

m-4m*m+10=0

Wy multiply elements

-4m^2+m+10=0

a = -4; b = 1; c = +10;
Δ = b2-4ac
Δ = 12-4·(-4)·10
Δ = 161
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{-(1)-\sqrt{161}}{2*-4}=\frac{-1-\sqrt{161}}{-8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{161}}{2*-4}=\frac{-1+\sqrt{161}}{-8}
$