1/4t+18=t

Solution for 1/4t+18=t equation:

1/4t+18=t

We move all terms to the left:

1/4t+18-(t)=0


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R


We add all the numbers together, and all the variables

-1t+1/4t+18=0

We multiply all the terms by the denominator


-1t*4t+18*4t+1=0

Wy multiply elements

-4t^2+72t+1=0

a = -4; b = 72; c = +1;
Δ = b2-4ac
Δ = 722-4·(-4)·1
Δ = 5200
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:

$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-20\sqrt{13}}{2*-4}=\frac{-72-20\sqrt{13}}{-8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+20\sqrt{13}}{2*-4}=\frac{-72+20\sqrt{13}}{-8}
$