9x+3=420/x

Solution for 9x+3=420/x equation:

9x+3=420/x

We move all terms to the left:

9x+3-(420/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9x-(+420/x)+3=0

We get rid of parentheses

9x-420/x+3=0

We multiply all the terms by the denominator


9x*x+3*x-420=0

We add all the numbers together, and all the variables

3x+9x*x-420=0

Wy multiply elements

9x^2+3x-420=0

a = 9; b = 3; c = -420;
Δ = b2-4ac
Δ = 32-4·9·(-420)
Δ = 15129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15129}=123$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-123}{2*9}=\frac{-126}{18}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+123}{2*9}=\frac{120}{18}
=6+2/3
$