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

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

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

We move all terms to the left:

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


Domain of the equation: 3)(x-1)!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+2x^2+2/3*-1)-5x+3=0

We multiply all the terms by the denominator


(+2x^2+2-5x*3*-1)+3*3*-1)=0

We add all the numbers together, and all the variables

(+2x^2+2-5x*3*-1)=0

We get rid of parentheses

2x^2-5x*3*+2-1=0

We add all the numbers together, and all the variables

2x^2-5x*3*+1=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-13x^2+1=0

a = -13; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-13)·1
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{13}}{2*-13}=\frac{0-2\sqrt{13}}{-26}
=-\frac{2\sqrt{13}}{-26}
=-\frac{\sqrt{13}}{-13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{13}}{2*-13}=\frac{0+2\sqrt{13}}{-26}
=\frac{2\sqrt{13}}{-26}
=\frac{\sqrt{13}}{-13}
$