1/3t-8=-3t+2

Solution for 1/3t-8=-3t+2 equation:

1/3t-8=-3t+2

We move all terms to the left:

1/3t-8-(-3t+2)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We get rid of parentheses

1/3t+3t-2-8=0

We multiply all the terms by the denominator


3t*3t-2*3t-8*3t+1=0

Wy multiply elements

9t^2-6t-24t+1=0

We add all the numbers together, and all the variables

9t^2-30t+1=0

a = 9; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·9·1
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-12\sqrt{6}}{2*9}=\frac{30-12\sqrt{6}}{18}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+12\sqrt{6}}{2*9}=\frac{30+12\sqrt{6}}{18}
$