5t-t=3+3/2t

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

5t-t=3+3/2t

We move all terms to the left:

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


Domain of the equation: 2t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

4t-(3/2t+3)=0

We get rid of parentheses

4t-3/2t-3=0

We multiply all the terms by the denominator


4t*2t-3*2t-3=0

Wy multiply elements

8t^2-6t-3=0

a = 8; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·8·(-3)
Δ = 132
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{33}}{2*8}=\frac{6-2\sqrt{33}}{16}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{33}}{2*8}=\frac{6+2\sqrt{33}}{16}
$