1/2t*4=t

Solution for 1/2t*4=t equation:

1/2t*4=t

We move all terms to the left:

1/2t*4-(t)=0


Domain of the equation: 2t*4!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

-1t+1/2t*4=0

We multiply all the terms by the denominator


-1t*2t*4+1=0

Wy multiply elements

-8t^2*4+1=0

Wy multiply elements

-32t^2+1=0

a = -32; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-32)·1
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{2}}{2*-32}=\frac{0-8\sqrt{2}}{-64}
=-\frac{8\sqrt{2}}{-64}
=-\frac{\sqrt{2}}{-8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{2}}{2*-32}=\frac{0+8\sqrt{2}}{-64}
=\frac{8\sqrt{2}}{-64}
=\frac{\sqrt{2}}{-8}
$