1/8t+3t-3=4

Solution for 1/8t+3t-3=4 equation:

1/8t+3t-3=4

We move all terms to the left:

1/8t+3t-3-(4)=0


Domain of the equation: 8t!=0

t!=0/8

t!=0

t∈R


We add all the numbers together, and all the variables

3t+1/8t-7=0

We multiply all the terms by the denominator


3t*8t-7*8t+1=0

Wy multiply elements

24t^2-56t+1=0

a = 24; b = -56; c = +1;
Δ = b2-4ac
Δ = -562-4·24·1
Δ = 3040
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:

$\sqrt{\Delta}=\sqrt{3040}=\sqrt{16*190}=\sqrt{16}*\sqrt{190}=4\sqrt{190}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{190}}{2*24}=\frac{56-4\sqrt{190}}{48}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{190}}{2*24}=\frac{56+4\sqrt{190}}{48}
$