3/5t2=4

Solution for 3/5t2=4 equation:

3/5t^2=4

We move all terms to the left:

3/5t^2-(4)=0


Domain of the equation: 5t^2!=0

t^2!=0/5

t^2!=√0

t!=0

t∈R


We multiply all the terms by the denominator


-4*5t^2+3=0

Wy multiply elements

-20t^2+3=0

a = -20; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-20)·3
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*-20}=\frac{0-4\sqrt{15}}{-40}
=-\frac{4\sqrt{15}}{-40}
=-\frac{\sqrt{15}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*-20}=\frac{0+4\sqrt{15}}{-40}
=\frac{4\sqrt{15}}{-40}
=\frac{\sqrt{15}}{-10}
$