3/5t+2=t

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

3/5t+2=t

We move all terms to the left:

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


Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R


We add all the numbers together, and all the variables

-1t+3/5t+2=0

We multiply all the terms by the denominator


-1t*5t+2*5t+3=0

Wy multiply elements

-5t^2+10t+3=0

a = -5; b = 10; c = +3;
Δ = b2-4ac
Δ = 102-4·(-5)·3
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{10}}{2*-5}=\frac{-10-4\sqrt{10}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{10}}{2*-5}=\frac{-10+4\sqrt{10}}{-10}
$