1/3t+1/2t=10

Solution for 1/3t+1/2t=10 equation:

1/3t+1/2t=10

We move all terms to the left:

1/3t+1/2t-(10)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R


We calculate fractions


2t/6t^2+3t/6t^2-10=0

We multiply all the terms by the denominator


2t+3t-10*6t^2=0

We add all the numbers together, and all the variables

5t-10*6t^2=0

Wy multiply elements

-60t^2+5t=0

a = -60; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-60)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-60}=\frac{-10}{-120}
=1/12
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-60}=\frac{0}{-120}
=0
$