4t^2/3=15-17^1/3

Solution for 4t^2/3=15-17^1/3 equation:

4t^2/3=15-17^1/3

We move all terms to the left:

4t^2/3-(15-17^1/3)=0

We get rid of parentheses

4t^2/3-15+17^1/3=0

We multiply all the terms by the denominator


4t^2-15*3+17^1=0

We add all the numbers together, and all the variables

4t^2-28=0

a = 4; b = 0; c = -28;
Δ = b2-4ac
Δ = 02-4·4·(-28)
Δ = 448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{7}}{2*4}=\frac{0-8\sqrt{7}}{8}
=-\frac{8\sqrt{7}}{8}
=-\sqrt{7}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{7}}{2*4}=\frac{0+8\sqrt{7}}{8}
=\frac{8\sqrt{7}}{8}
=\sqrt{7}
$