(1/2)6t^2=24t

Solution for (1/2)6t^2=24t equation:

(1/2)6t^2=24t

We move all terms to the left:

(1/2)6t^2-(24t)=0


Domain of the equation: 2)6t^2!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

(+1/2)6t^2-24t=0

We add all the numbers together, and all the variables

-24t+(+1/2)6t^2=0

We multiply all the terms by the denominator


-24t*2)6t^2+(+1=0

Wy multiply elements

-48t^2+1=0

a = -48; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-48)·1
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*-48}=\frac{0-8\sqrt{3}}{-96}
=-\frac{8\sqrt{3}}{-96}
=-\frac{\sqrt{3}}{-12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*-48}=\frac{0+8\sqrt{3}}{-96}
=\frac{8\sqrt{3}}{-96}
=\frac{\sqrt{3}}{-12}
$