1/8t+34t-3=4

Solution for 1/8t+34t-3=4 equation:

1/8t+34t-3=4

We move all terms to the left:

1/8t+34t-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

34t+1/8t-7=0

We multiply all the terms by the denominator


34t*8t-7*8t+1=0

Wy multiply elements

272t^2-56t+1=0

a = 272; b = -56; c = +1;
Δ = b2-4ac
Δ = -562-4·272·1
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-32\sqrt{2}}{2*272}=\frac{56-32\sqrt{2}}{544}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+32\sqrt{2}}{2*272}=\frac{56+32\sqrt{2}}{544}
$