2/3x-5=-2x

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

2/3x-5=-2x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x+2x-5=0

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-15x+2=0

a = 6; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·6·2
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{177}}{2*6}=\frac{15-\sqrt{177}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{177}}{2*6}=\frac{15+\sqrt{177}}{12}
$