2m=1/4m-7

Solution for 2m=1/4m-7 equation:

2m=1/4m-7

We move all terms to the left:

2m-(1/4m-7)=0


Domain of the equation: 4m-7)!=0

m∈R


We get rid of parentheses

2m-1/4m+7=0

We multiply all the terms by the denominator


2m*4m+7*4m-1=0

Wy multiply elements

8m^2+28m-1=0

a = 8; b = 28; c = -1;
Δ = b2-4ac
Δ = 282-4·8·(-1)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{51}}{2*8}=\frac{-28-4\sqrt{51}}{16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{51}}{2*8}=\frac{-28+4\sqrt{51}}{16}
$