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

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
$