(21/8x+30)4=(51/3x)3

Solution for (21/8x+30)4=(51/3x)3 equation:

(21/8x+30)4=(51/3x)3

We move all terms to the left:

(21/8x+30)4-((51/3x)3)=0


Domain of the equation: 8x+30)4!=0

x∈R



Domain of the equation: 3x)3)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(21/8x+30)4-((+51/3x)3)=0

We multiply parentheses

84x-((+51/3x)3)+120=0

We multiply all the terms by the denominator


84x*3x)3)-((+120*3x)3)+51=0

Wy multiply elements

252x^2+360x=0

a = 252; b = 360; c = 0;
Δ = b2-4ac
Δ = 3602-4·252·0
Δ = 129600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{129600}=360$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-360}{2*252}=\frac{-720}{504}
=-1+3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+360}{2*252}=\frac{0}{504}
=0
$