2t+8+1/5t-t=11

Solution for 2t+8+1/5t-t=11 equation:

2t+8+1/5t-t=11

We move all terms to the left:

2t+8+1/5t-t-(11)=0


Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R


We add all the numbers together, and all the variables

t+1/5t-3=0

We multiply all the terms by the denominator


t*5t-3*5t+1=0

Wy multiply elements

5t^2-15t+1=0

a = 5; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·5·1
Δ = 205
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{205}}{2*5}=\frac{15-\sqrt{205}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{205}}{2*5}=\frac{15+\sqrt{205}}{10}
$