1/3t+2/5t=33

Solution for 1/3t+2/5t=33 equation:

1/3t+2/5t=33

We move all terms to the left:

1/3t+2/5t-(33)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R


We calculate fractions


5t/15t^2+6t/15t^2-33=0

We multiply all the terms by the denominator


5t+6t-33*15t^2=0

We add all the numbers together, and all the variables

11t-33*15t^2=0

Wy multiply elements

-495t^2+11t=0

a = -495; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-495)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-495}=\frac{-22}{-990}
=1/45
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-495}=\frac{0}{-990}
=0
$