3/2t+7/t=1

Solution for 3/2t+7/t=1 equation:

3/2t+7/t=1

We move all terms to the left:

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


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: t!=0

t∈R


We calculate fractions


3t/2t^2+14t/2t^2-1=0

We multiply all the terms by the denominator


3t+14t-1*2t^2=0

We add all the numbers together, and all the variables

17t-1*2t^2=0

Wy multiply elements

-2t^2+17t=0

a = -2; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-2)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-2}=\frac{-34}{-4}
=8+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-2}=\frac{0}{-4}
=0
$