3/5*t=2

Solution for 3/5*t=2 equation:

3/5*t=2

We move all terms to the left:

3/5*t-(2)=0


Domain of the equation: 5*t!=0

t!=0/1

t!=0

t∈R


We multiply all the terms by the denominator


-2*5*t+3=0

Wy multiply elements

-10t*t+3=0

Wy multiply elements

-10t^2+3=0

a = -10; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-10)·3
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*-10}=\frac{0-2\sqrt{30}}{-20}
=-\frac{2\sqrt{30}}{-20}
=-\frac{\sqrt{30}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*-10}=\frac{0+2\sqrt{30}}{-20}
=\frac{2\sqrt{30}}{-20}
=\frac{\sqrt{30}}{-10}
$