2t+10/t=12

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

2t+10/t=12

We move all terms to the left:

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


Domain of the equation: t!=0

t∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

2t^2-12t+10=0

a = 2; b = -12; c = +10;
Δ = b2-4ac
Δ = -122-4·2·10
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8}{2*2}=\frac{4}{4}
=1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8}{2*2}=\frac{20}{4}
=5
$