2/3x+2.5=-x

Solution for 2/3x+2.5=-x equation:

2/3x+2.5=-x

We move all terms to the left:

2/3x+2.5-(-x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(-1x)+2.5=0

We get rid of parentheses

2/3x+1x+2.5=0

We multiply all the terms by the denominator


1x*3x+(2.5)*3x+2=0

We multiply parentheses

1x*3x+7.5x+2=0

Wy multiply elements

3x^2+7.5x+2=0

a = 3; b = 7.5; c = +2;
Δ = b2-4ac
Δ = 7.52-4·3·2
Δ = 32.25
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{-(7.5)-\sqrt{32.25}}{2*3}=\frac{-7.5-\sqrt{32.25}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7.5)+\sqrt{32.25}}{2*3}=\frac{-7.5+\sqrt{32.25}}{6}
$