5/t=t/45t=

Solution for 5/t=t/45t= equation:

5/t=t/45t=

We move all terms to the left:

5/t-(t/45t)=0


Domain of the equation: t!=0

t∈R



Domain of the equation: 45t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

5/t-(+t/45t)=0

We get rid of parentheses

5/t-t/45t=0

We calculate fractions


(-1t^2)/45t^2+225t/45t^2=0

We multiply all the terms by the denominator


(-1t^2)+225t=0

We get rid of parentheses

-1t^2+225t=0

a = -1; b = 225; c = 0;
Δ = b2-4ac
Δ = 2252-4·(-1)·0
Δ = 50625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{50625}=225$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(225)-225}{2*-1}=\frac{-450}{-2}
=+225
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(225)+225}{2*-1}=\frac{0}{-2}
=0
$