2+0.8x=9/10x

Solution for 2+0.8x=9/10x equation:

2+0.8x=9/10x

We move all terms to the left:

2+0.8x-(9/10x)=0


Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

0.8x-(+9/10x)+2=0

We get rid of parentheses

0.8x-9/10x+2=0

We multiply all the terms by the denominator


(0.8x)*10x+2*10x-9=0

We add all the numbers together, and all the variables

(+0.8x)*10x+2*10x-9=0

We multiply parentheses

0x^2+2*10x-9=0

Wy multiply elements

0x^2+20x-9=0

We add all the numbers together, and all the variables

x^2+20x-9=0

a = 1; b = 20; c = -9;
Δ = b2-4ac
Δ = 202-4·1·(-9)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{109}}{2*1}=\frac{-20-2\sqrt{109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{109}}{2*1}=\frac{-20+2\sqrt{109}}{2}
$