1/3x+1/4x=57

Solution for 1/3x+1/4x=57 equation:

1/3x+1/4x=57

We move all terms to the left:

1/3x+1/4x-(57)=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+3x/12x^2-57=0

We multiply all the terms by the denominator


4x+3x-57*12x^2=0

We add all the numbers together, and all the variables

7x-57*12x^2=0

Wy multiply elements

-684x^2+7x=0

a = -684; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-684)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-684}=\frac{-14}{-1368}
=7/684
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-684}=\frac{0}{-1368}
=0
$