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

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

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

We move all terms to the left:

2t+8t+1/2t-t-(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

9t+1/2t-11=0

We multiply all the terms by the denominator


9t*2t-11*2t+1=0

Wy multiply elements

18t^2-22t+1=0

a = 18; b = -22; c = +1;
Δ = b2-4ac
Δ = -222-4·18·1
Δ = 412
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:

$\sqrt{\Delta}=\sqrt{412}=\sqrt{4*103}=\sqrt{4}*\sqrt{103}=2\sqrt{103}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{103}}{2*18}=\frac{22-2\sqrt{103}}{36}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{103}}{2*18}=\frac{22+2\sqrt{103}}{36}
$