2/5x+1/10x+6=11

Solution for 2/5x+1/10x+6=11 equation:

2/5x+1/10x+6=11

We move all terms to the left:

2/5x+1/10x+6-(11)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


20x/50x^2+5x/50x^2-5=0

We multiply all the terms by the denominator


20x+5x-5*50x^2=0

We add all the numbers together, and all the variables

25x-5*50x^2=0

Wy multiply elements

-250x^2+25x=0

a = -250; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-250)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-250}=\frac{-50}{-500}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-250}=\frac{0}{-500}
=0
$