5m=8/2m-6

Solution for 5m=8/2m-6 equation:

5m=8/2m-6

We move all terms to the left:

5m-(8/2m-6)=0


Domain of the equation: 2m-6)!=0

m∈R


We get rid of parentheses

5m-8/2m+6=0

We multiply all the terms by the denominator


5m*2m+6*2m-8=0

Wy multiply elements

10m^2+12m-8=0

a = 10; b = 12; c = -8;
Δ = b2-4ac
Δ = 122-4·10·(-8)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{29}}{2*10}=\frac{-12-4\sqrt{29}}{20}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{29}}{2*10}=\frac{-12+4\sqrt{29}}{20}
$