16+16t^2/4t=3*5t-6

Solution for 16+16t^2/4t=3*5t-6 equation:

16+16t^2/4t=3*5t-6

We move all terms to the left:

16+16t^2/4t-(3*5t-6)=0


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R


We get rid of parentheses

16t^2/4t-3*5t+6+16=0

We multiply all the terms by the denominator


16t^2-(3*5t)*4t+6*4t+16*4t=0

We add all the numbers together, and all the variables

16t^2-(+3*5t)*4t+6*4t+16*4t=0

We multiply parentheses

16t^2-60t^2+6*4t+16*4t=0

Wy multiply elements

16t^2-60t^2+24t+64t=0

We add all the numbers together, and all the variables

-44t^2+88t=0

a = -44; b = 88; c = 0;
Δ = b2-4ac
Δ = 882-4·(-44)·0
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-88}{2*-44}=\frac{-176}{-88}
=+2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+88}{2*-44}=\frac{0}{-88}
=0
$