2/3t-2+1/2t=5

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

2/3t-2+1/2t=5

We move all terms to the left:

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

2/3t+1/2t-7=0

We calculate fractions


4t/6t^2+3t/6t^2-7=0

We multiply all the terms by the denominator


4t+3t-7*6t^2=0

We add all the numbers together, and all the variables

7t-7*6t^2=0

Wy multiply elements

-42t^2+7t=0

a = -42; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-42)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-42}=\frac{-14}{-84}
=1/6
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-42}=\frac{0}{-84}
=0
$