4t=60/10t

Solution for 4t=60/10t equation:

4t=60/10t

We move all terms to the left:

4t-(60/10t)=0


Domain of the equation: 10t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

4t-(+60/10t)=0

We get rid of parentheses

4t-60/10t=0

We multiply all the terms by the denominator


4t*10t-60=0

Wy multiply elements

40t^2-60=0

a = 40; b = 0; c = -60;
Δ = b2-4ac
Δ = 02-4·40·(-60)
Δ = 9600
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:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{6}}{2*40}=\frac{0-40\sqrt{6}}{80}
=-\frac{40\sqrt{6}}{80}
=-\frac{\sqrt{6}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{6}}{2*40}=\frac{0+40\sqrt{6}}{80}
=\frac{40\sqrt{6}}{80}
=\frac{\sqrt{6}}{2}
$