1/2x-5=4/3x+10

Solution for 1/2x-5=4/3x+10 equation:

1/2x-5=4/3x+10

We move all terms to the left:

1/2x-5-(4/3x+10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x+10)!=0

x∈R


We get rid of parentheses

1/2x-4/3x-10-5=0

We calculate fractions


3x/6x^2+(-8x)/6x^2-10-5=0

We add all the numbers together, and all the variables

3x/6x^2+(-8x)/6x^2-15=0

We multiply all the terms by the denominator


3x+(-8x)-15*6x^2=0

Wy multiply elements

-90x^2+3x+(-8x)=0

We get rid of parentheses

-90x^2+3x-8x=0

We add all the numbers together, and all the variables

-90x^2-5x=0

a = -90; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-90)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-90}=\frac{0}{-180}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-90}=\frac{10}{-180}
=-1/18
$