7/8m+5-2/9m=52

Solution for 7/8m+5-2/9m=52 equation:

7/8m+5-2/9m=52

We move all terms to the left:

7/8m+5-2/9m-(52)=0


Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R



Domain of the equation: 9m!=0

m!=0/9

m!=0

m∈R


We add all the numbers together, and all the variables

7/8m-2/9m-47=0

We calculate fractions


63m/72m^2+(-16m)/72m^2-47=0

We multiply all the terms by the denominator


63m+(-16m)-47*72m^2=0

Wy multiply elements

-3384m^2+63m+(-16m)=0

We get rid of parentheses

-3384m^2+63m-16m=0

We add all the numbers together, and all the variables

-3384m^2+47m=0

a = -3384; b = 47; c = 0;
Δ = b2-4ac
Δ = 472-4·(-3384)·0
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-47}{2*-3384}=\frac{-94}{-6768}
=1/72
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+47}{2*-3384}=\frac{0}{-6768}
=0
$