2/5x+4=-1/6x+8

Solution for 2/5x+4=-1/6x+8 equation:

2/5x+4=-1/6x+8

We move all terms to the left:

2/5x+4-(-1/6x+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x+8)!=0

x∈R


We get rid of parentheses

2/5x+1/6x-8+4=0

We calculate fractions


12x/30x^2+5x/30x^2-8+4=0

We add all the numbers together, and all the variables

12x/30x^2+5x/30x^2-4=0

We multiply all the terms by the denominator


12x+5x-4*30x^2=0

We add all the numbers together, and all the variables

17x-4*30x^2=0

Wy multiply elements

-120x^2+17x=0

a = -120; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-120)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-120}=\frac{-34}{-240}
=17/120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-120}=\frac{0}{-240}
=0
$