4/5m-2=m-3

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

4/5m-2=m-3

We move all terms to the left:

4/5m-2-(m-3)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R


We get rid of parentheses

4/5m-m+3-2=0

We multiply all the terms by the denominator


-m*5m+3*5m-2*5m+4=0

Wy multiply elements

-5m^2+15m-10m+4=0

We add all the numbers together, and all the variables

-5m^2+5m+4=0

a = -5; b = 5; c = +4;
Δ = b2-4ac
Δ = 52-4·(-5)·4
Δ = 105
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{-(5)-\sqrt{105}}{2*-5}=\frac{-5-\sqrt{105}}{-10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{105}}{2*-5}=\frac{-5+\sqrt{105}}{-10}
$