5/12x+2/3x=37

Solution for 5/12x+2/3x=37 equation:

5/12x+2/3x=37

We move all terms to the left:

5/12x+2/3x-(37)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


15x/36x^2+24x/36x^2-37=0

We multiply all the terms by the denominator


15x+24x-37*36x^2=0

We add all the numbers together, and all the variables

39x-37*36x^2=0

Wy multiply elements

-1332x^2+39x=0

a = -1332; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·(-1332)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*-1332}=\frac{-78}{-2664}
=13/444
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*-1332}=\frac{0}{-2664}
=0
$