x=3/45x+3=9x

Solution for x=3/45x+3=9x equation:

x=3/45x+3=9x

We move all terms to the left:

x-(3/45x+3)=0


Domain of the equation: 45x+3)!=0

x∈R


We get rid of parentheses

x-3/45x-3=0

We multiply all the terms by the denominator


x*45x-3*45x-3=0

Wy multiply elements

45x^2-135x-3=0

a = 45; b = -135; c = -3;
Δ = b2-4ac
Δ = -1352-4·45·(-3)
Δ = 18765
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:

$\sqrt{\Delta}=\sqrt{18765}=\sqrt{9*2085}=\sqrt{9}*\sqrt{2085}=3\sqrt{2085}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-3\sqrt{2085}}{2*45}=\frac{135-3\sqrt{2085}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+3\sqrt{2085}}{2*45}=\frac{135+3\sqrt{2085}}{90}
$