-5/3m-7/4m=-287/24

Solution for -5/3m-7/4m=-287/24 equation:

-5/3m-7/4m=-287/24

We move all terms to the left:

-5/3m-7/4m-(-287/24)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R


We get rid of parentheses

-5/3m-7/4m+287/24=0

We calculate fractions


13776m^2/576m^2+(-960m)/576m^2+(-1008m)/576m^2=0

We multiply all the terms by the denominator


13776m^2+(-960m)+(-1008m)=0

We get rid of parentheses

13776m^2-960m-1008m=0

We add all the numbers together, and all the variables

13776m^2-1968m=0

a = 13776; b = -1968; c = 0;
Δ = b2-4ac
Δ = -19682-4·13776·0
Δ = 3873024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3873024}=1968$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1968)-1968}{2*13776}=\frac{0}{27552}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1968)+1968}{2*13776}=\frac{3936}{27552}
=1/7
$