12-4/3t=t

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

12-4/3t=t

We move all terms to the left:

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


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We add all the numbers together, and all the variables

-1t-4/3t+12=0

We multiply all the terms by the denominator


-1t*3t+12*3t-4=0

Wy multiply elements

-3t^2+36t-4=0

a = -3; b = 36; c = -4;
Δ = b2-4ac
Δ = 362-4·(-3)·(-4)
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{78}}{2*-3}=\frac{-36-4\sqrt{78}}{-6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{78}}{2*-3}=\frac{-36+4\sqrt{78}}{-6}
$