2/5x+6=1/10x-7

Solution for 2/5x+6=1/10x-7 equation:

2/5x+6=1/10x-7

We move all terms to the left:

2/5x+6-(1/10x-7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x-7)!=0

x∈R


We get rid of parentheses

2/5x-1/10x+7+6=0

We calculate fractions


20x/50x^2+(-5x)/50x^2+7+6=0

We add all the numbers together, and all the variables

20x/50x^2+(-5x)/50x^2+13=0

We multiply all the terms by the denominator


20x+(-5x)+13*50x^2=0

Wy multiply elements

650x^2+20x+(-5x)=0

We get rid of parentheses

650x^2+20x-5x=0

We add all the numbers together, and all the variables

650x^2+15x=0

a = 650; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·650·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*650}=\frac{-30}{1300}
=-3/130
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*650}=\frac{0}{1300}
=0
$