3x=54/3x+15=21

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Solution for 3x=54/3x+15=21 equation: 



3x=54/3x+15=21

We move all terms to the left:

3x-(54/3x+15)=0



Domain of the equation: 3x+15)!=0

x∈R



We get rid of parentheses

3x-54/3x-15=0

We multiply all the terms by the denominator


3x*3x-15*3x-54=0

Wy multiply elements

9x^2-45x-54=0

a = 9; b = -45; c = -54;
Δ = b2-4ac
Δ = -452-4·9·(-54)
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-63}{2*9}=\frac{-18}{18}
=-1
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+63}{2*9}=\frac{108}{18}
=6
$

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