7/4m-5/6=3/5m+25

Solution for 7/4m-5/6=3/5m+25 equation:

7/4m-5/6=3/5m+25

We move all terms to the left:

7/4m-5/6-(3/5m+25)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 5m+25)!=0

m∈R


We get rid of parentheses

7/4m-3/5m-25-5/6=0

We calculate fractions


(-500m^2)/720m^2+1260m/720m^2+(-432m)/720m^2-25=0

We multiply all the terms by the denominator


(-500m^2)+1260m+(-432m)-25*720m^2=0

Wy multiply elements

(-500m^2)-18000m^2+1260m+(-432m)=0

We get rid of parentheses

-500m^2-18000m^2+1260m-432m=0

We add all the numbers together, and all the variables

-18500m^2+828m=0

a = -18500; b = 828; c = 0;
Δ = b2-4ac
Δ = 8282-4·(-18500)·0
Δ = 685584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{685584}=828$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(828)-828}{2*-18500}=\frac{-1656}{-37000}
=207/4625
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(828)+828}{2*-18500}=\frac{0}{-37000}
=0
$