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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We get rid of parentheses

-120x^2+9x-4x=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{-10}{-240}
=1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-120}=\frac{0}{-240}
=0
$