3/t-3=8/2t-5

Solution for 3/t-3=8/2t-5 equation:

3/t-3=8/2t-5

We move all terms to the left:

3/t-3-(8/2t-5)=0


Domain of the equation: t!=0

t∈R



Domain of the equation: 2t-5)!=0

t∈R


We get rid of parentheses

3/t-8/2t+5-3=0

We calculate fractions


6t/2t^2+(-8t)/2t^2+5-3=0

We add all the numbers together, and all the variables

6t/2t^2+(-8t)/2t^2+2=0

We multiply all the terms by the denominator


6t+(-8t)+2*2t^2=0

Wy multiply elements

4t^2+6t+(-8t)=0

We get rid of parentheses

4t^2+6t-8t=0

We add all the numbers together, and all the variables

4t^2-2t=0

a = 4; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·4·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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