1/4m+5/7m=6

Solution for 1/4m+5/7m=6 equation:

1/4m+5/7m=6

We move all terms to the left:

1/4m+5/7m-(6)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 7m!=0

m!=0/7

m!=0

m∈R


We calculate fractions


7m/28m^2+20m/28m^2-6=0

We multiply all the terms by the denominator


7m+20m-6*28m^2=0

We add all the numbers together, and all the variables

27m-6*28m^2=0

Wy multiply elements

-168m^2+27m=0

a = -168; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-168)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-168}=\frac{-54}{-336}
=9/56
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-168}=\frac{0}{-336}
=0
$