5/12t+3=t-21

Solution for 5/12t+3=t-21 equation:

5/12t+3=t-21

We move all terms to the left:

5/12t+3-(t-21)=0


Domain of the equation: 12t!=0

t!=0/12

t!=0

t∈R


We get rid of parentheses

5/12t-t+21+3=0

We multiply all the terms by the denominator


-t*12t+21*12t+3*12t+5=0

Wy multiply elements

-12t^2+252t+36t+5=0

We add all the numbers together, and all the variables

-12t^2+288t+5=0

a = -12; b = 288; c = +5;
Δ = b2-4ac
Δ = 2882-4·(-12)·5
Δ = 83184
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:

$\sqrt{\Delta}=\sqrt{83184}=\sqrt{16*5199}=\sqrt{16}*\sqrt{5199}=4\sqrt{5199}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-4\sqrt{5199}}{2*-12}=\frac{-288-4\sqrt{5199}}{-24}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+4\sqrt{5199}}{2*-12}=\frac{-288+4\sqrt{5199}}{-24}
$