65-t=(2)/(3)t

Solution for 65-t=(2)/(3)t equation:

65-t=(2)/(3)t

We move all terms to the left:

65-t-((2)/(3)t)=0


Domain of the equation: 3t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

-t-(+2/3t)+65=0

We add all the numbers together, and all the variables

-1t-(+2/3t)+65=0

We get rid of parentheses

-1t-2/3t+65=0

We multiply all the terms by the denominator


-1t*3t+65*3t-2=0

Wy multiply elements

-3t^2+195t-2=0

a = -3; b = 195; c = -2;
Δ = b2-4ac
Δ = 1952-4·(-3)·(-2)
Δ = 38001
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{-(195)-\sqrt{38001}}{2*-3}=\frac{-195-\sqrt{38001}}{-6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(195)+\sqrt{38001}}{2*-3}=\frac{-195+\sqrt{38001}}{-6}
$