2/5x+5=-2/6x+1

Solution for 2/5x+5=-2/6x+1 equation:

2/5x+5=-2/6x+1

We move all terms to the left:

2/5x+5-(-2/6x+1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x+1)!=0

x∈R


We get rid of parentheses

2/5x+2/6x-1+5=0

We calculate fractions


12x/30x^2+10x/30x^2-1+5=0

We add all the numbers together, and all the variables

12x/30x^2+10x/30x^2+4=0

We multiply all the terms by the denominator


12x+10x+4*30x^2=0

We add all the numbers together, and all the variables

22x+4*30x^2=0

Wy multiply elements

120x^2+22x=0

a = 120; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·120·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*120}=\frac{-44}{240}
=-11/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*120}=\frac{0}{240}
=0
$