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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-120x^2+4x+(-9x)=0

We get rid of parentheses

-120x^2+4x-9x=0

We add all the numbers together, and all the variables

-120x^2-5x=0

a = -120; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-120)·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*-120}=\frac{0}{-240}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-120}=\frac{10}{-240}
=-1/24
$