1/4t+6=t

Solution for 1/4t+6=t equation:

1/4t+6=t

We move all terms to the left:

1/4t+6-(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+6=0

We multiply all the terms by the denominator


-1t*4t+6*4t+1=0

Wy multiply elements

-4t^2+24t+1=0

a = -4; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·(-4)·1
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{37}}{2*-4}=\frac{-24-4\sqrt{37}}{-8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{37}}{2*-4}=\frac{-24+4\sqrt{37}}{-8}
$