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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x+11)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-5x)/10x^2+(-2x)/10x^2-11+3=0

We add all the numbers together, and all the variables

(-5x)/10x^2+(-2x)/10x^2-8=0

We multiply all the terms by the denominator


(-5x)+(-2x)-8*10x^2=0

Wy multiply elements

-80x^2+(-5x)+(-2x)=0

We get rid of parentheses

-80x^2-5x-2x=0

We add all the numbers together, and all the variables

-80x^2-7x=0

a = -80; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-80)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-80}=\frac{0}{-160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-80}=\frac{14}{-160}
=-7/80
$