.6(m-30)=2/3m+20

Solution for .6(m-30)=2/3m+20 equation:

.6(m-30)=2/3m+20

We move all terms to the left:

.6(m-30)-(2/3m+20)=0


Domain of the equation: 3m+20)!=0

m∈R


We multiply parentheses

0.6m-(2/3m+20)-18=0

We get rid of parentheses

0.6m-2/3m-20-18=0

We multiply all the terms by the denominator


(0.6m)*3m-20*3m-18*3m-2=0

We add all the numbers together, and all the variables

(+0.6m)*3m-20*3m-18*3m-2=0

We multiply parentheses

0m^2-20*3m-18*3m-2=0

Wy multiply elements

0m^2-60m-54m-2=0

We add all the numbers together, and all the variables

m^2-114m-2=0

a = 1; b = -114; c = -2;
Δ = b2-4ac
Δ = -1142-4·1·(-2)
Δ = 13004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{13004}=\sqrt{4*3251}=\sqrt{4}*\sqrt{3251}=2\sqrt{3251}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-2\sqrt{3251}}{2*1}=\frac{114-2\sqrt{3251}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+2\sqrt{3251}}{2*1}=\frac{114+2\sqrt{3251}}{2}
$