12-1/5t=2t+1

Solution for 12-1/5t=2t+1 equation:

12-1/5t=2t+1

We move all terms to the left:

12-1/5t-(2t+1)=0


Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R


We get rid of parentheses

-1/5t-2t-1+12=0

We multiply all the terms by the denominator


-2t*5t-1*5t+12*5t-1=0

Wy multiply elements

-10t^2-5t+60t-1=0

We add all the numbers together, and all the variables

-10t^2+55t-1=0

a = -10; b = 55; c = -1;
Δ = b2-4ac
Δ = 552-4·(-10)·(-1)
Δ = 2985
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-\sqrt{2985}}{2*-10}=\frac{-55-\sqrt{2985}}{-20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{2985}}{2*-10}=\frac{-55+\sqrt{2985}}{-20}
$