X+24=5/4x

Solution for X+24=5/4x equation:

X+24=5/4X

We move all terms to the left:

X+24-(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)+24=0

We get rid of parentheses

X-5/4X+24=0

We multiply all the terms by the denominator


X*4X+24*4X-5=0

Wy multiply elements

4X^2+96X-5=0

a = 4; b = 96; c = -5;
Δ = b2-4ac
Δ = 962-4·4·(-5)
Δ = 9296
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:

$\sqrt{\Delta}=\sqrt{9296}=\sqrt{16*581}=\sqrt{16}*\sqrt{581}=4\sqrt{581}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-4\sqrt{581}}{2*4}=\frac{-96-4\sqrt{581}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+4\sqrt{581}}{2*4}=\frac{-96+4\sqrt{581}}{8}
$