(1/3)x+(1/4)x+x=57

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

(1/3)x+(1/4)x+x=57

We move all terms to the left:

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


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

x^2+x^2+x-57=0

We add all the numbers together, and all the variables

2x^2+x-57=0

a = 2; b = 1; c = -57;
Δ = b2-4ac
Δ = 12-4·2·(-57)
Δ = 457
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{457}}{2*2}=\frac{-1-\sqrt{457}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{457}}{2*2}=\frac{-1+\sqrt{457}}{4}
$