20-2t=1/2t=28

Solution for 20-2t=1/2t=28 equation:

20-2t=1/2t=28

We move all terms to the left:

20-2t-(1/2t)=0


Domain of the equation: 2t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

-2t-(+1/2t)+20=0

We get rid of parentheses

-2t-1/2t+20=0

We multiply all the terms by the denominator


-2t*2t+20*2t-1=0

Wy multiply elements

-4t^2+40t-1=0

a = -4; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·(-4)·(-1)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-12\sqrt{11}}{2*-4}=\frac{-40-12\sqrt{11}}{-8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+12\sqrt{11}}{2*-4}=\frac{-40+12\sqrt{11}}{-8}
$