1/3x+1/4x-1/2=-3

Solution for 1/3x+1/4x-1/2=-3 equation:

1/3x+1/4x-1/2=-3

We move all terms to the left:

1/3x+1/4x-1/2-(-3)=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 add all the numbers together, and all the variables

1/3x+1/4x+3-1/2=0

We calculate fractions


(-48x^2)/48x^2+16x/48x^2+12x/48x^2+3=0

We multiply all the terms by the denominator


(-48x^2)+16x+12x+3*48x^2=0

We add all the numbers together, and all the variables

(-48x^2)+28x+3*48x^2=0

Wy multiply elements

(-48x^2)+144x^2+28x=0

We get rid of parentheses

-48x^2+144x^2+28x=0

We add all the numbers together, and all the variables

96x^2+28x=0

a = 96; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·96·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*96}=\frac{-56}{192}
=-7/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*96}=\frac{0}{192}
=0
$