2/3x-5=3x+5

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

2/3x-5=3x+5

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-3x-5-5=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-9x^2-30x+2=0

a = -9; b = -30; c = +2;
Δ = b2-4ac
Δ = -302-4·(-9)·2
Δ = 972
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:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-18\sqrt{3}}{2*-9}=\frac{30-18\sqrt{3}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+18\sqrt{3}}{2*-9}=\frac{30+18\sqrt{3}}{-18}
$