-4/3m-5/2-29/8m=-97/15

Solution for -4/3m-5/2-29/8m=-97/15 equation:

-4/3m-5/2-29/8m=-97/15

We move all terms to the left:

-4/3m-5/2-29/8m-(-97/15)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R


We get rid of parentheses

-4/3m-29/8m-5/2+97/15=0

We calculate fractions


(-14400m^2)/1440m^2+37248m^2/1440m^2+(-1920m)/1440m^2+(-5220m)/1440m^2=0

We multiply all the terms by the denominator


(-14400m^2)+37248m^2+(-1920m)+(-5220m)=0

We add all the numbers together, and all the variables

37248m^2+(-14400m^2)+(-1920m)+(-5220m)=0

We get rid of parentheses

37248m^2-14400m^2-1920m-5220m=0

We add all the numbers together, and all the variables

22848m^2-7140m=0

a = 22848; b = -7140; c = 0;
Δ = b2-4ac
Δ = -71402-4·22848·0
Δ = 50979600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{50979600}=7140$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7140)-7140}{2*22848}=\frac{0}{45696}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7140)+7140}{2*22848}=\frac{14280}{45696}
=5/16
$