2/5x+3=-5/2x

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

2/5x+3=-5/2x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

2/5x+5/2x+3=0

We calculate fractions


4x/10x^2+25x/10x^2+3=0

We multiply all the terms by the denominator


4x+25x+3*10x^2=0

We add all the numbers together, and all the variables

29x+3*10x^2=0

Wy multiply elements

30x^2+29x=0

a = 30; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·30·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*30}=\frac{-58}{60}
=-29/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*30}=\frac{0}{60}
=0
$