7m-2/4m-2=2/1

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

7m-2/4m-2=2/1

We move all terms to the left:

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


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R


We add all the numbers together, and all the variables

7m-2/4m-2-0=0

We add all the numbers together, and all the variables

7m-2/4m-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

28m^2-8m-2=0

a = 28; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·28·(-2)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12\sqrt{2}}{2*28}=\frac{8-12\sqrt{2}}{56}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12\sqrt{2}}{2*28}=\frac{8+12\sqrt{2}}{56}
$