150/t=6t

Solution for 150/t=6t equation:

150/t=6t

We move all terms to the left:

150/t-(6t)=0


Domain of the equation: t!=0

t∈R


We add all the numbers together, and all the variables

-6t+150/t=0

We multiply all the terms by the denominator


-6t*t+150=0

Wy multiply elements

-6t^2+150=0

a = -6; b = 0; c = +150;
Δ = b2-4ac
Δ = 02-4·(-6)·150
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60}{2*-6}=\frac{-60}{-12}
=+5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60}{2*-6}=\frac{60}{-12}
=-5
$