1/2x-5=10-2/3x

Solution for 1/2x-5=10-2/3x equation:

1/2x-5=10-2/3x

We move all terms to the left:

1/2x-5-(10-2/3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-2/3x+10)-5=0

We get rid of parentheses

1/2x+2/3x-10-5=0

We calculate fractions


3x/6x^2+4x/6x^2-10-5=0

We add all the numbers together, and all the variables

3x/6x^2+4x/6x^2-15=0

We multiply all the terms by the denominator


3x+4x-15*6x^2=0

We add all the numbers together, and all the variables

7x-15*6x^2=0

Wy multiply elements

-90x^2+7x=0

a = -90; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-90)·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*-90}=\frac{-14}{-180}
=7/90
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-90}=\frac{0}{-180}
=0
$