5x^2/3=32

Solution for 5x^2/3=32 equation:

5x^2/3=32

We move all terms to the left:

5x^2/3-(32)=0

We multiply all the terms by the denominator


5x^2-32*3=0

We add all the numbers together, and all the variables

5x^2-96=0

a = 5; b = 0; c = -96;
Δ = b2-4ac
Δ = 02-4·5·(-96)
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{30}}{2*5}=\frac{0-8\sqrt{30}}{10}
=-\frac{8\sqrt{30}}{10}
=-\frac{4\sqrt{30}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{30}}{2*5}=\frac{0+8\sqrt{30}}{10}
=\frac{8\sqrt{30}}{10}
=\frac{4\sqrt{30}}{5}
$