x+17=4/9*x

Solution for x+17=4/9*x equation:

x+17=4/9x

We move all terms to the left:

x+17-(4/9x)=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+4/9x)+17=0

We get rid of parentheses

x-4/9x+17=0

We multiply all the terms by the denominator


x*9x+17*9x-4=0

Wy multiply elements

9x^2+153x-4=0

a = 9; b = 153; c = -4;
Δ = b2-4ac
Δ = 1532-4·9·(-4)
Δ = 23553
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:

$\sqrt{\Delta}=\sqrt{23553}=\sqrt{9*2617}=\sqrt{9}*\sqrt{2617}=3\sqrt{2617}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(153)-3\sqrt{2617}}{2*9}=\frac{-153-3\sqrt{2617}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(153)+3\sqrt{2617}}{2*9}=\frac{-153+3\sqrt{2617}}{18}
$