3/t+4=12+3t

Solution for 3/t+4=12+3t equation:

3/t+4=12+3t

We move all terms to the left:

3/t+4-(12+3t)=0


Domain of the equation: t!=0

t∈R


We add all the numbers together, and all the variables

3/t-(3t+12)+4=0

We get rid of parentheses

3/t-3t-12+4=0

We multiply all the terms by the denominator


-3t*t-12*t+4*t+3=0

We add all the numbers together, and all the variables

-8t-3t*t+3=0

Wy multiply elements

-3t^2-8t+3=0

a = -3; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·(-3)·3
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-10}{2*-3}=\frac{-2}{-6}
=1/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+10}{2*-3}=\frac{18}{-6}
=-3
$