2-5x-8=20+3/4x

Solution for 2-5x-8=20+3/4x equation:

2-5x-8=20+3/4x

We move all terms to the left:

2-5x-8-(20+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+20)+2-8=0

We add all the numbers together, and all the variables

-5x-(3/4x+20)-6=0

We get rid of parentheses

-5x-3/4x-20-6=0

We multiply all the terms by the denominator


-5x*4x-20*4x-6*4x-3=0

Wy multiply elements

-20x^2-80x-24x-3=0

We add all the numbers together, and all the variables

-20x^2-104x-3=0

a = -20; b = -104; c = -3;
Δ = b2-4ac
Δ = -1042-4·(-20)·(-3)
Δ = 10576
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:

$\sqrt{\Delta}=\sqrt{10576}=\sqrt{16*661}=\sqrt{16}*\sqrt{661}=4\sqrt{661}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-4\sqrt{661}}{2*-20}=\frac{104-4\sqrt{661}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+4\sqrt{661}}{2*-20}=\frac{104+4\sqrt{661}}{-40}
$