6/10x-1.5=8.9+0.2x

Solution for 6/10x-1.5=8.9+0.2x equation:

6/10x-1.5=8.9+0.2x

We move all terms to the left:

6/10x-1.5-(8.9+0.2x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

6/10x-(0.2x+8.9)-1.5=0

We get rid of parentheses

6/10x-0.2x-8.9-1.5=0

We multiply all the terms by the denominator


-(0.2x)*10x-(8.9)*10x-(1.5)*10x+6=0

We add all the numbers together, and all the variables

-(+0.2x)*10x-(8.9)*10x-(1.5)*10x+6=0

We multiply parentheses

-0x^2-89x-15x+6=0

We add all the numbers together, and all the variables

-1x^2-104x+6=0

a = -1; b = -104; c = +6;
Δ = b2-4ac
Δ = -1042-4·(-1)·6
Δ = 10840
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:

$\sqrt{\Delta}=\sqrt{10840}=\sqrt{4*2710}=\sqrt{4}*\sqrt{2710}=2\sqrt{2710}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-2\sqrt{2710}}{2*-1}=\frac{104-2\sqrt{2710}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+2\sqrt{2710}}{2*-1}=\frac{104+2\sqrt{2710}}{-2}
$