8/5m+20=1/10m-25

Solution for 8/5m+20=1/10m-25 equation:

8/5m+20=1/10m-25

We move all terms to the left:

8/5m+20-(1/10m-25)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R



Domain of the equation: 10m-25)!=0

m∈R


We get rid of parentheses

8/5m-1/10m+25+20=0

We calculate fractions


80m/50m^2+(-5m)/50m^2+25+20=0

We add all the numbers together, and all the variables

80m/50m^2+(-5m)/50m^2+45=0

We multiply all the terms by the denominator


80m+(-5m)+45*50m^2=0

Wy multiply elements

2250m^2+80m+(-5m)=0

We get rid of parentheses

2250m^2+80m-5m=0

We add all the numbers together, and all the variables

2250m^2+75m=0

a = 2250; b = 75; c = 0;
Δ = b2-4ac
Δ = 752-4·2250·0
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-75}{2*2250}=\frac{-150}{4500}
=-1/30
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+75}{2*2250}=\frac{0}{4500}
=0
$