2t+8+1/2t-1=11

Solution for 2t+8+1/2t-1=11 equation:

2t+8+1/2t-1=11

We move all terms to the left:

2t+8+1/2t-1-(11)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R


We add all the numbers together, and all the variables

2t+1/2t-4=0

We multiply all the terms by the denominator


2t*2t-4*2t+1=0

Wy multiply elements

4t^2-8t+1=0

a = 4; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·4·1
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{3}}{2*4}=\frac{8-4\sqrt{3}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{3}}{2*4}=\frac{8+4\sqrt{3}}{8}
$