0.9x-20=2/3x

Solution for 0.9x-20=2/3x equation:

0.9x-20=2/3x

We move all terms to the left:

0.9x-20-(2/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

0.9x-(+2/3x)-20=0

We get rid of parentheses

0.9x-2/3x-20=0

We multiply all the terms by the denominator


(0.9x)*3x-20*3x-2=0

We add all the numbers together, and all the variables

(+0.9x)*3x-20*3x-2=0

We multiply parentheses

0x^2-20*3x-2=0

Wy multiply elements

0x^2-60x-2=0

We add all the numbers together, and all the variables

x^2-60x-2=0

a = 1; b = -60; c = -2;
Δ = b2-4ac
Δ = -602-4·1·(-2)
Δ = 3608
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:

$\sqrt{\Delta}=\sqrt{3608}=\sqrt{4*902}=\sqrt{4}*\sqrt{902}=2\sqrt{902}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{902}}{2*1}=\frac{60-2\sqrt{902}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{902}}{2*1}=\frac{60+2\sqrt{902}}{2}
$