2m-6/2m=10

Solution for 2m-6/2m=10 equation:

2m-6/2m=10

We move all terms to the left:

2m-6/2m-(10)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We multiply all the terms by the denominator


2m*2m-10*2m-6=0

Wy multiply elements

4m^2-20m-6=0

a = 4; b = -20; c = -6;
Δ = b2-4ac
Δ = -202-4·4·(-6)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{31}}{2*4}=\frac{20-4\sqrt{31}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{31}}{2*4}=\frac{20+4\sqrt{31}}{8}
$