1/3t=t-145

Solution for 1/3t=t-145 equation:

1/3t=t-145

We move all terms to the left:

1/3t-(t-145)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We get rid of parentheses

1/3t-t+145=0

We multiply all the terms by the denominator


-t*3t+145*3t+1=0

Wy multiply elements

-3t^2+435t+1=0

a = -3; b = 435; c = +1;
Δ = b2-4ac
Δ = 4352-4·(-3)·1
Δ = 189237
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{-(435)-\sqrt{189237}}{2*-3}=\frac{-435-\sqrt{189237}}{-6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(435)+\sqrt{189237}}{2*-3}=\frac{-435+\sqrt{189237}}{-6}
$