5x+9=3/7x

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Solution for 5x+9=3/7x equation: 



5x+9=3/7x

We move all terms to the left:

5x+9-(3/7x)=0



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R



We add all the numbers together, and all the variables

5x-(+3/7x)+9=0

We get rid of parentheses

5x-3/7x+9=0

We multiply all the terms by the denominator


5x*7x+9*7x-3=0

Wy multiply elements

35x^2+63x-3=0

a = 35; b = 63; c = -3;
Δ = b2-4ac
Δ = 632-4·35·(-3)
Δ = 4389
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-\sqrt{4389}}{2*35}=\frac{-63-\sqrt{4389}}{70}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+\sqrt{4389}}{2*35}=\frac{-63+\sqrt{4389}}{70}
$

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