8-1/2x+4=0.6x+3-0.2x

Solution for 8-1/2x+4=0.6x+3-0.2x equation:

8-1/2x+4=0.6x+3-0.2x

We move all terms to the left:

8-1/2x+4-(0.6x+3-0.2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1/2x-(0.4x+3)+8+4=0

We add all the numbers together, and all the variables

-1/2x-(0.4x+3)+12=0

We get rid of parentheses

-1/2x-0.4x-3+12=0

We multiply all the terms by the denominator


-(0.4x)*2x-3*2x+12*2x-1=0

We add all the numbers together, and all the variables

-(+0.4x)*2x-3*2x+12*2x-1=0

We multiply parentheses

-0x^2-3*2x+12*2x-1=0

Wy multiply elements

-0x^2-6x+24x-1=0

We add all the numbers together, and all the variables

-1x^2+18x-1=0

a = -1; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·(-1)·(-1)
Δ = 320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-8\sqrt{5}}{2*-1}=\frac{-18-8\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+8\sqrt{5}}{2*-1}=\frac{-18+8\sqrt{5}}{-2}
$