4/5x-0.6x+0.3=x-9

Solution for 4/5x-0.6x+0.3=x-9 equation:

4/5x-0.6x+0.3=x-9

We move all terms to the left:

4/5x-0.6x+0.3-(x-9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-0.6x+4/5x-(x-9)+0.3=0

We get rid of parentheses

-0.6x+4/5x-x+9+0.3=0

We multiply all the terms by the denominator


-(0.6x)*5x-x*5x+9*5x+(0.3)*5x+4=0

We add all the numbers together, and all the variables

-(+0.6x)*5x-x*5x+9*5x+(0.3)*5x+4=0

We multiply parentheses

-0x^2-x*5x+9*5x+1.5x+4=0

Wy multiply elements

-0x^2-5x^2+45x+1.5x+4=0

We add all the numbers together, and all the variables

-6x^2+46.5x+4=0

a = -6; b = 46.5; c = +4;
Δ = b2-4ac
Δ = 46.52-4·(-6)·4
Δ = 2258.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46.5)-\sqrt{2258.25}}{2*-6}=\frac{-46.5-\sqrt{2258.25}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46.5)+\sqrt{2258.25}}{2*-6}=\frac{-46.5+\sqrt{2258.25}}{-12}
$