5x-2=(5x^2-6x)/3x

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Solution for 5x-2=(5x^2-6x)/3x equation: 



5x-2=(5x^2-6x)/3x

We move all terms to the left:

5x-2-((5x^2-6x)/3x)=0



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R



We multiply all the terms by the denominator


5x*3x)-((5x^2-6x)-2*3x)=0

Wy multiply elements

15x^2-6x=0

a = 15; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·15·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*15}=\frac{0}{30}
=0
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*15}=\frac{12}{30}
=2/5
$

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