14m-7+3/5m=4.8-3.8m

Solution for 14m-7+3/5m=4.8-3.8m equation:

14m-7+3/5m=4.8-3.8m

We move all terms to the left:

14m-7+3/5m-(4.8-3.8m)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R


We add all the numbers together, and all the variables

14m+3/5m-(-3.8m+4.8)-7=0

We get rid of parentheses

14m+3/5m+3.8m-4.8-7=0

We multiply all the terms by the denominator


14m*5m+(3.8m)*5m-(4.8)*5m-7*5m+3=0

We add all the numbers together, and all the variables

14m*5m+(+3.8m)*5m-(4.8)*5m-7*5m+3=0

We multiply parentheses

15m^2+14m*5m-24m-7*5m+3=0

Wy multiply elements

15m^2+70m^2-24m-35m+3=0

We add all the numbers together, and all the variables

85m^2-59m+3=0

a = 85; b = -59; c = +3;
Δ = b2-4ac
Δ = -592-4·85·3
Δ = 2461
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-\sqrt{2461}}{2*85}=\frac{59-\sqrt{2461}}{170}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{2461}}{2*85}=\frac{59+\sqrt{2461}}{170}
$