X+6=5/4x

Solution for X+6=5/4x equation:

X+6=5/4X

We move all terms to the left:

X+6-(5/4X)=0


Domain of the equation: 4X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+5/4X)+6=0

We get rid of parentheses

X-5/4X+6=0

We multiply all the terms by the denominator


X*4X+6*4X-5=0

Wy multiply elements

4X^2+24X-5=0

a = 4; b = 24; c = -5;
Δ = b2-4ac
Δ = 242-4·4·(-5)
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{41}}{2*4}=\frac{-24-4\sqrt{41}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{41}}{2*4}=\frac{-24+4\sqrt{41}}{8}
$