9x2/3=13.5

Solution for 9x2/3=13.5 equation:

9x^2/3=13.5

We move all terms to the left:

9x^2/3-(13.5)=0

We add all the numbers together, and all the variables

9x^2/3-13.5=0

We multiply all the terms by the denominator


9x^2-(13.5)*3=0

We add all the numbers together, and all the variables

9x^2-40.5=0

a = 9; b = 0; c = -40.5;
Δ = b2-4ac
Δ = 02-4·9·(-40.5)
Δ = 1458
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:

$\sqrt{\Delta}=\sqrt{1458}=\sqrt{729*2}=\sqrt{729}*\sqrt{2}=27\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-27\sqrt{2}}{2*9}=\frac{0-27\sqrt{2}}{18}
=-\frac{27\sqrt{2}}{18}
=-\frac{3\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+27\sqrt{2}}{2*9}=\frac{0+27\sqrt{2}}{18}
=\frac{27\sqrt{2}}{18}
=\frac{3\sqrt{2}}{2}
$