-9=2/3*x-17

Solution for -9=2/3*x-17 equation:

-9=2/3*x-17

We move all terms to the left:

-9-(2/3*x-17)=0


Domain of the equation: 3*x-17)!=0

x∈R


We get rid of parentheses

-2/3*x+17-9=0

We multiply all the terms by the denominator


17*3*x-9*3*x-2=0

Wy multiply elements

51x*x-27x*x-2=0

Wy multiply elements

51x^2-27x^2-2=0

We add all the numbers together, and all the variables

24x^2-2=0

a = 24; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·24·(-2)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*24}=\frac{0-8\sqrt{3}}{48}
=-\frac{8\sqrt{3}}{48}
=-\frac{\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*24}=\frac{0+8\sqrt{3}}{48}
=\frac{8\sqrt{3}}{48}
=\frac{\sqrt{3}}{6}
$