4/7x+5/12x=39

Solution for 4/7x+5/12x=39 equation:

4/7x+5/12x=39

We move all terms to the left:

4/7x+5/12x-(39)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We calculate fractions


48x/84x^2+35x/84x^2-39=0

We multiply all the terms by the denominator


48x+35x-39*84x^2=0

We add all the numbers together, and all the variables

83x-39*84x^2=0

Wy multiply elements

-3276x^2+83x=0

a = -3276; b = 83; c = 0;
Δ = b2-4ac
Δ = 832-4·(-3276)·0
Δ = 6889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6889}=83$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(83)-83}{2*-3276}=\frac{-166}{-6552}
=83/3276
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(83)+83}{2*-3276}=\frac{0}{-6552}
=0
$