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

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



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

We move all terms to the left:

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



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

x∈R





Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R



We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

84x-51/3x+120=0

We multiply all the terms by the denominator


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

Wy multiply elements

252x^2+360x-51=0

a = 252; b = 360; c = -51;
Δ = b2-4ac
Δ = 3602-4·252·(-51)
Δ = 181008
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:


$\sqrt{\Delta}=\sqrt{181008}=\sqrt{144*1257}=\sqrt{144}*\sqrt{1257}=12\sqrt{1257}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-12\sqrt{1257}}{2*252}=\frac{-360-12\sqrt{1257}}{504}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+12\sqrt{1257}}{2*252}=\frac{-360+12\sqrt{1257}}{504}
$

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