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

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

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

We move all terms to the left:

5t+2+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

4t+1/2t-9=0

We multiply all the terms by the denominator


4t*2t-9*2t+1=0

Wy multiply elements

8t^2-18t+1=0

a = 8; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·8·1
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{73}}{2*8}=\frac{18-2\sqrt{73}}{16}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{73}}{2*8}=\frac{18+2\sqrt{73}}{16}
$