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

Solution for (2/3)x+1=15/9 equation:

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

We move all terms to the left:

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


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

2x^2+1-15/9=0

We multiply all the terms by the denominator


2x^2*9-15+1*9=0

We add all the numbers together, and all the variables

2x^2*9-6=0

Wy multiply elements

18x^2-6=0

a = 18; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·18·(-6)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*18}=\frac{0-12\sqrt{3}}{36}
=-\frac{12\sqrt{3}}{36}
=-\frac{\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*18}=\frac{0+12\sqrt{3}}{36}
=\frac{12\sqrt{3}}{36}
=\frac{\sqrt{3}}{3}
$