2/3m-0.5m+4=7

Solution for 2/3m-0.5m+4=7 equation:

2/3m-0.5m+4=7

We move all terms to the left:

2/3m-0.5m+4-(7)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We add all the numbers together, and all the variables

-0.5m+2/3m-3=0

We multiply all the terms by the denominator


-(0.5m)*3m-3*3m+2=0

We add all the numbers together, and all the variables

-(+0.5m)*3m-3*3m+2=0

We multiply parentheses

-0m^2-3*3m+2=0

Wy multiply elements

-0m^2-9m+2=0

We add all the numbers together, and all the variables

-1m^2-9m+2=0

a = -1; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·(-1)·2
Δ = 89
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{-(-9)-\sqrt{89}}{2*-1}=\frac{9-\sqrt{89}}{-2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{89}}{2*-1}=\frac{9+\sqrt{89}}{-2}
$