4/7x+15/4x=39

Solution for 4/7x+15/4x=39 equation:

4/7x+15/4x=39

We move all terms to the left:

4/7x+15/4x-(39)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


16x/28x^2+105x/28x^2-39=0

We multiply all the terms by the denominator


16x+105x-39*28x^2=0

We add all the numbers together, and all the variables

121x-39*28x^2=0

Wy multiply elements

-1092x^2+121x=0

a = -1092; b = 121; c = 0;
Δ = b2-4ac
Δ = 1212-4·(-1092)·0
Δ = 14641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14641}=121$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(121)-121}{2*-1092}=\frac{-242}{-2184}
=121/1092
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(121)+121}{2*-1092}=\frac{0}{-2184}
=0
$