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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


4x/12x^2+(-9x)/12x^2+5-10=0

We add all the numbers together, and all the variables

4x/12x^2+(-9x)/12x^2-5=0

We multiply all the terms by the denominator


4x+(-9x)-5*12x^2=0

Wy multiply elements

-60x^2+4x+(-9x)=0

We get rid of parentheses

-60x^2+4x-9x=0

We add all the numbers together, and all the variables

-60x^2-5x=0

a = -60; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-60)·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*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-60}=\frac{10}{-120}
=-1/12
$