9x^2/3-5=139

Solution for 9x^2/3-5=139 equation:

9x^2/3-5=139

We move all terms to the left:

9x^2/3-5-(139)=0

We add all the numbers together, and all the variables

9x^2/3-144=0

We multiply all the terms by the denominator


9x^2-144*3=0

We add all the numbers together, and all the variables

9x^2-432=0

a = 9; b = 0; c = -432;
Δ = b2-4ac
Δ = 02-4·9·(-432)
Δ = 15552
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:

$\sqrt{\Delta}=\sqrt{15552}=\sqrt{5184*3}=\sqrt{5184}*\sqrt{3}=72\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{3}}{2*9}=\frac{0-72\sqrt{3}}{18}
=-\frac{72\sqrt{3}}{18}
=-4\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{3}}{2*9}=\frac{0+72\sqrt{3}}{18}
=\frac{72\sqrt{3}}{18}
=4\sqrt{3}
$