1/2x+5=3/5x-6

Solution for 1/2x+5=3/5x-6 equation:

1/2x+5=3/5x-6

We move all terms to the left:

1/2x+5-(3/5x-6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x-6)!=0

x∈R


We get rid of parentheses

1/2x-3/5x+6+5=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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