-1/6t+1=2t-10

Solution for -1/6t+1=2t-10 equation:

-1/6t+1=2t-10

We move all terms to the left:

-1/6t+1-(2t-10)=0


Domain of the equation: 6t!=0

t!=0/6

t!=0

t∈R


We get rid of parentheses

-1/6t-2t+10+1=0

We multiply all the terms by the denominator


-2t*6t+10*6t+1*6t-1=0

Wy multiply elements

-12t^2+60t+6t-1=0

We add all the numbers together, and all the variables

-12t^2+66t-1=0

a = -12; b = 66; c = -1;
Δ = b2-4ac
Δ = 662-4·(-12)·(-1)
Δ = 4308
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:

$\sqrt{\Delta}=\sqrt{4308}=\sqrt{4*1077}=\sqrt{4}*\sqrt{1077}=2\sqrt{1077}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1077}}{2*-12}=\frac{-66-2\sqrt{1077}}{-24}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1077}}{2*-12}=\frac{-66+2\sqrt{1077}}{-24}
$