t/16t+24=4t+64

Solution for t/16t+24=4t+64 equation:

t/16t+24=4t+64

We move all terms to the left:

t/16t+24-(4t+64)=0


Domain of the equation: 16t!=0

t!=0/16

t!=0

t∈R


We get rid of parentheses

t/16t-4t-64+24=0

We multiply all the terms by the denominator


t-4t*16t-64*16t+24*16t=0

Wy multiply elements

-64t^2+t-1024t+384t=0

We add all the numbers together, and all the variables

-64t^2-639t=0

a = -64; b = -639; c = 0;
Δ = b2-4ac
Δ = -6392-4·(-64)·0
Δ = 408321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{408321}=639$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-639)-639}{2*-64}=\frac{0}{-128}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-639)+639}{2*-64}=\frac{1278}{-128}
=-9+63/64
$