4/5m-2=-9/10m+3

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Solution for 4/5m-2=-9/10m+3 equation:



4/5m-2=-9/10m+3
We move all terms to the left:
4/5m-2-(-9/10m+3)=0
Domain of the equation: 5m!=0
m!=0/5
m!=0
m∈R
Domain of the equation: 10m+3)!=0
m∈R
We get rid of parentheses
4/5m+9/10m-3-2=0
We calculate fractions
40m/50m^2+45m/50m^2-3-2=0
We add all the numbers together, and all the variables
40m/50m^2+45m/50m^2-5=0
We multiply all the terms by the denominator
40m+45m-5*50m^2=0
We add all the numbers together, and all the variables
85m-5*50m^2=0
Wy multiply elements
-250m^2+85m=0
a = -250; b = 85; c = 0;
Δ = b2-4ac
Δ = 852-4·(-250)·0
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-85}{2*-250}=\frac{-170}{-500} =17/50 $
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+85}{2*-250}=\frac{0}{-500} =0 $

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