8/5t+1/2t=20

Solution for 8/5t+1/2t=20 equation:

8/5t+1/2t=20

We move all terms to the left:

8/5t+1/2t-(20)=0


Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R



Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R


We calculate fractions


16t/10t^2+5t/10t^2-20=0

We multiply all the terms by the denominator


16t+5t-20*10t^2=0

We add all the numbers together, and all the variables

21t-20*10t^2=0

Wy multiply elements

-200t^2+21t=0

a = -200; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-200)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-200}=\frac{-42}{-400}
=21/200
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-200}=\frac{0}{-400}
=0
$