3/5x-1/2x=-11

Solution for 3/5x-1/2x=-11 equation:

3/5x-1/2x=-11

We move all terms to the left:

3/5x-1/2x-(-11)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-1/2x+11=0

We calculate fractions


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

We multiply all the terms by the denominator


6x+(-5x)+11*10x^2=0

Wy multiply elements

110x^2+6x+(-5x)=0

We get rid of parentheses

110x^2+6x-5x=0

We add all the numbers together, and all the variables

110x^2+x=0

a = 110; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·110·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*110}=\frac{-2}{220}
=-1/110
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*110}=\frac{0}{220}
=0
$