15t=120/t=8

Solution for 15t=120/t=8 equation:

15t=120/t=8

We move all terms to the left:

15t-(120/t)=0


Domain of the equation: t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

15t-(+120/t)=0

We get rid of parentheses

15t-120/t=0

We multiply all the terms by the denominator


15t*t-120=0

Wy multiply elements

15t^2-120=0

a = 15; b = 0; c = -120;
Δ = b2-4ac
Δ = 02-4·15·(-120)
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{2}}{2*15}=\frac{0-60\sqrt{2}}{30}
=-\frac{60\sqrt{2}}{30}
=-2\sqrt{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{2}}{2*15}=\frac{0+60\sqrt{2}}{30}
=\frac{60\sqrt{2}}{30}
=2\sqrt{2}
$