2t+10=12/t

Solution for 2t+10=12/t equation:

2t+10=12/t

We move all terms to the left:

2t+10-(12/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

2t-(+12/t)+10=0

We get rid of parentheses

2t-12/t+10=0

We multiply all the terms by the denominator


2t*t+10*t-12=0

We add all the numbers together, and all the variables

10t+2t*t-12=0

Wy multiply elements

2t^2+10t-12=0

a = 2; b = 10; c = -12;
Δ = b2-4ac
Δ = 102-4·2·(-12)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*2}=\frac{-24}{4}
=-6
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*2}=\frac{4}{4}
=1
$