1x-39=3/4x

Solution for 1x-39=3/4x equation:

1x-39=3/4x

We move all terms to the left:

1x-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

1x-(+3/4x)-39=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

x-3/4x-39=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-156x-3=0

a = 4; b = -156; c = -3;
Δ = b2-4ac
Δ = -1562-4·4·(-3)
Δ = 24384
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:

$\sqrt{\Delta}=\sqrt{24384}=\sqrt{64*381}=\sqrt{64}*\sqrt{381}=8\sqrt{381}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-8\sqrt{381}}{2*4}=\frac{156-8\sqrt{381}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+8\sqrt{381}}{2*4}=\frac{156+8\sqrt{381}}{8}
$