12t/3t+13=5*17t

Solution for 12t/3t+13=5*17t equation:

12t/3t+13=5*17t

We move all terms to the left:

12t/3t+13-(5*17t)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We add all the numbers together, and all the variables

12t/3t-(+5*17t)+13=0

We get rid of parentheses

12t/3t-5*17t+13=0

We multiply all the terms by the denominator


12t-(5*17t)*3t+13*3t=0

We add all the numbers together, and all the variables

12t-(+5*17t)*3t+13*3t=0

We multiply parentheses

-255t^2+12t+13*3t=0

Wy multiply elements

-255t^2+12t+39t=0

We add all the numbers together, and all the variables

-255t^2+51t=0

a = -255; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·(-255)·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*-255}=\frac{-102}{-510}
=1/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*-255}=\frac{0}{-510}
=0
$