4/7m-7=3/4m-13

Solution for 4/7m-7=3/4m-13 equation:

4/7m-7=3/4m-13

We move all terms to the left:

4/7m-7-(3/4m-13)=0


Domain of the equation: 7m!=0

m!=0/7

m!=0

m∈R



Domain of the equation: 4m-13)!=0

m∈R


We get rid of parentheses

4/7m-3/4m+13-7=0

We calculate fractions


16m/28m^2+(-21m)/28m^2+13-7=0

We add all the numbers together, and all the variables

16m/28m^2+(-21m)/28m^2+6=0

We multiply all the terms by the denominator


16m+(-21m)+6*28m^2=0

Wy multiply elements

168m^2+16m+(-21m)=0

We get rid of parentheses

168m^2+16m-21m=0

We add all the numbers together, and all the variables

168m^2-5m=0

a = 168; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·168·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*168}=\frac{0}{336}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*168}=\frac{10}{336}
=5/168
$