25/6m-5/3m=7

Solution for 25/6m-5/3m=7 equation:

25/6m-5/3m=7

We move all terms to the left:

25/6m-5/3m-(7)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R



Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We calculate fractions


75m/18m^2+(-30m)/18m^2-7=0

We multiply all the terms by the denominator


75m+(-30m)-7*18m^2=0

Wy multiply elements

-126m^2+75m+(-30m)=0

We get rid of parentheses

-126m^2+75m-30m=0

We add all the numbers together, and all the variables

-126m^2+45m=0

a = -126; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-126)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*-126}=\frac{-90}{-252}
=5/14
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-126}=\frac{0}{-252}
=0
$