(2/3)x-(1/9)x+5=20

Solution for (2/3)x-(1/9)x+5=20 equation:

(2/3)x-(1/9)x+5=20

We move all terms to the left:

(2/3)x-(1/9)x+5-(20)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 9)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/3)x-(+1/9)x+5-20=0

We add all the numbers together, and all the variables

(+2/3)x-(+1/9)x-15=0

We multiply parentheses

2x^2-x^2-15=0

We add all the numbers together, and all the variables

x^2-15=0

a = 1; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·1·(-15)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*1}=\frac{0-2\sqrt{15}}{2}
=-\frac{2\sqrt{15}}{2}
=-\sqrt{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*1}=\frac{0+2\sqrt{15}}{2}
=\frac{2\sqrt{15}}{2}
=\sqrt{15}
$