1/3t-1/2t-4=-14

Solution for 1/3t-1/2t-4=-14 equation:

1/3t-1/2t-4=-14

We move all terms to the left:

1/3t-1/2t-4-(-14)=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 add all the numbers together, and all the variables

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

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

Wy multiply elements

60t^2+2t+(-3t)=0

We get rid of parentheses

60t^2+2t-3t=0

We add all the numbers together, and all the variables

60t^2-1t=0

a = 60; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·60·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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