36-5x=1/4x+1

Solution for 36-5x=1/4x+1 equation:

36-5x=1/4x+1

We move all terms to the left:

36-5x-(1/4x+1)=0


Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

-5x-1/4x-1+36=0

We multiply all the terms by the denominator


-5x*4x-1*4x+36*4x-1=0

Wy multiply elements

-20x^2-4x+144x-1=0

We add all the numbers together, and all the variables

-20x^2+140x-1=0

a = -20; b = 140; c = -1;
Δ = b2-4ac
Δ = 1402-4·(-20)·(-1)
Δ = 19520
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:

$\sqrt{\Delta}=\sqrt{19520}=\sqrt{64*305}=\sqrt{64}*\sqrt{305}=8\sqrt{305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-8\sqrt{305}}{2*-20}=\frac{-140-8\sqrt{305}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+8\sqrt{305}}{2*-20}=\frac{-140+8\sqrt{305}}{-40}
$