2/3t-6=9-t

Solution for 2/3t-6=9-t equation:

2/3t-6=9-t

We move all terms to the left:

2/3t-6-(9-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

2/3t-(-1t+9)-6=0

We get rid of parentheses

2/3t+1t-9-6=0

We multiply all the terms by the denominator


1t*3t-9*3t-6*3t+2=0

Wy multiply elements

3t^2-27t-18t+2=0

We add all the numbers together, and all the variables

3t^2-45t+2=0

a = 3; b = -45; c = +2;
Δ = b2-4ac
Δ = -452-4·3·2
Δ = 2001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{2001}}{2*3}=\frac{45-\sqrt{2001}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2001}}{2*3}=\frac{45+\sqrt{2001}}{6}
$