10/x-3=3/4x

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

10/x-3=3/4x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10/x-(+3/4x)-3=0

We get rid of parentheses

10/x-3/4x-3=0

We calculate fractions


40x/4x^2+(-3x)/4x^2-3=0

We multiply all the terms by the denominator


40x+(-3x)-3*4x^2=0

Wy multiply elements

-12x^2+40x+(-3x)=0

We get rid of parentheses

-12x^2+40x-3x=0

We add all the numbers together, and all the variables

-12x^2+37x=0

a = -12; b = 37; c = 0;
Δ = b2-4ac
Δ = 372-4·(-12)·0
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-37}{2*-12}=\frac{-74}{-24}
=3+1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+37}{2*-12}=\frac{0}{-24}
=0
$