(1/3)*x+(1/4)=1

Solution for (1/3)*x+(1/4)=1 equation:

(1/3)*x+(1/4)=1

We move all terms to the left:

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


Domain of the equation: 3)*x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
(1/3)*x-1+(1/4)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

x^2-1+1/4=0

We multiply all the terms by the denominator


x^2*4+1-1*4=0

We add all the numbers together, and all the variables

x^2*4-3=0

Wy multiply elements

4x^2-3=0

a = 4; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·4·(-3)
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*4}=\frac{0-4\sqrt{3}}{8}
=-\frac{4\sqrt{3}}{8}
=-\frac{\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*4}=\frac{0+4\sqrt{3}}{8}
=\frac{4\sqrt{3}}{8}
=\frac{\sqrt{3}}{2}
$