85=5x2/3

Solution for 85=5x2/3 equation:

85=5x^2/3

We move all terms to the left:

85-(5x^2/3)=0

We get rid of parentheses

-5x^2/3+85=0

We multiply all the terms by the denominator


-5x^2+85*3=0

We add all the numbers together, and all the variables

-5x^2+255=0

a = -5; b = 0; c = +255;
Δ = b2-4ac
Δ = 02-4·(-5)·255
Δ = 5100
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:

$\sqrt{\Delta}=\sqrt{5100}=\sqrt{100*51}=\sqrt{100}*\sqrt{51}=10\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{51}}{2*-5}=\frac{0-10\sqrt{51}}{-10}
=-\frac{10\sqrt{51}}{-10}
=-\frac{\sqrt{51}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{51}}{2*-5}=\frac{0+10\sqrt{51}}{-10}
=\frac{10\sqrt{51}}{-10}
=\frac{\sqrt{51}}{-1}
$