y2/3-10(y1/2)+16=0

Solution for y2/3-10(y1/2)+16=0 equation:

y2/3-10(y1/2)+16=0

We add all the numbers together, and all the variables

y2/3-10(+y1/2)+16=0

We multiply parentheses

y2/3-10y+16=0

We multiply all the terms by the denominator


y2-10y*3+16*3=0

We add all the numbers together, and all the variables

y^2-10y*3+48=0

Wy multiply elements

y^2-30y+48=0

a = 1; b = -30; c = +48;
Δ = b2-4ac
Δ = -302-4·1·48
Δ = 708
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{708}=\sqrt{4*177}=\sqrt{4}*\sqrt{177}=2\sqrt{177}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{177}}{2*1}=\frac{30-2\sqrt{177}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{177}}{2*1}=\frac{30+2\sqrt{177}}{2}
$