1.5m-1.65=6m-8-5/6m

Solution for 1.5m-1.65=6m-8-5/6m equation:

1.5m-1.65=6m-8-5/6m

We move all terms to the left:

1.5m-1.65-(6m-8-5/6m)=0


Domain of the equation: 6m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

1.5m-(6m-5/6m-8)-1.65=0

We get rid of parentheses

1.5m-6m+5/6m+8-1.65=0

We multiply all the terms by the denominator


(1.5m)*6m-6m*6m+8*6m-(1.65)*6m+5=0

We add all the numbers together, and all the variables

(+1.5m)*6m-6m*6m+8*6m-(1.65)*6m+5=0

We multiply parentheses

6m^2-6m*6m+8*6m-9.9m+5=0

Wy multiply elements

6m^2-36m^2+48m-9.9m+5=0

We add all the numbers together, and all the variables

-30m^2+38.1m+5=0

a = -30; b = 38.1; c = +5;
Δ = b2-4ac
Δ = 38.12-4·(-30)·5
Δ = 2051.61
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{-(38.1)-\sqrt{2051.61}}{2*-30}=\frac{-38.1-\sqrt{2051.61}}{-60}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38.1)+\sqrt{2051.61}}{2*-30}=\frac{-38.1+\sqrt{2051.61}}{-60}
$