3/8*t=48

Solution for 3/8*t=48 equation:

3/8*t=48

We move all terms to the left:

3/8*t-(48)=0


Domain of the equation: 8*t!=0

t!=0/1

t!=0

t∈R


We multiply all the terms by the denominator


-48*8*t+3=0

Wy multiply elements

-384t*t+3=0

Wy multiply elements

-384t^2+3=0

a = -384; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-384)·3
Δ = 4608
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:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{2}}{2*-384}=\frac{0-48\sqrt{2}}{-768}
=-\frac{48\sqrt{2}}{-768}
=-\frac{\sqrt{2}}{-16}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{2}}{2*-384}=\frac{0+48\sqrt{2}}{-768}
=\frac{48\sqrt{2}}{-768}
=\frac{\sqrt{2}}{-16}
$