5x+39=3/4x

Solution for 5x+39=3/4x equation:

5x+39=3/4x

We move all terms to the left:

5x+39-(3/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+3/4x)+39=0

We get rid of parentheses

5x-3/4x+39=0

We multiply all the terms by the denominator


5x*4x+39*4x-3=0

Wy multiply elements

20x^2+156x-3=0

a = 20; b = 156; c = -3;
Δ = b2-4ac
Δ = 1562-4·20·(-3)
Δ = 24576
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:

$\sqrt{\Delta}=\sqrt{24576}=\sqrt{4096*6}=\sqrt{4096}*\sqrt{6}=64\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-64\sqrt{6}}{2*20}=\frac{-156-64\sqrt{6}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+64\sqrt{6}}{2*20}=\frac{-156+64\sqrt{6}}{40}
$