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

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

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

We move all terms to the left:

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


Domain of the equation: 2t-t)!=0

t∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2t+1t-1/2t-8=0

We multiply all the terms by the denominator


2t*2t+1t*2t-8*2t-1=0

Wy multiply elements

4t^2+2t^2-16t-1=0

We add all the numbers together, and all the variables

6t^2-16t-1=0

a = 6; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·6·(-1)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{70}}{2*6}=\frac{16-2\sqrt{70}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{70}}{2*6}=\frac{16+2\sqrt{70}}{12}
$