2/5x+15x=x-6

Solution for 2/5x+15x=x-6 equation:

2/5x+15x=x-6

We move all terms to the left:

2/5x+15x-(x-6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

15x+2/5x-(x-6)=0

We get rid of parentheses

15x+2/5x-x+6=0

We multiply all the terms by the denominator


15x*5x-x*5x+6*5x+2=0

Wy multiply elements

75x^2-5x^2+30x+2=0

We add all the numbers together, and all the variables

70x^2+30x+2=0

a = 70; b = 30; c = +2;
Δ = b2-4ac
Δ = 302-4·70·2
Δ = 340
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{85}}{2*70}=\frac{-30-2\sqrt{85}}{140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{85}}{2*70}=\frac{-30+2\sqrt{85}}{140}
$