20-1/5t=3/10t+16

Solution for 20-1/5t=3/10t+16 equation:

20-1/5t=3/10t+16

We move all terms to the left:

20-1/5t-(3/10t+16)=0


Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R



Domain of the equation: 10t+16)!=0

t∈R


We get rid of parentheses

-1/5t-3/10t-16+20=0

We calculate fractions


(-10t)/50t^2+(-15t)/50t^2-16+20=0

We add all the numbers together, and all the variables

(-10t)/50t^2+(-15t)/50t^2+4=0

We multiply all the terms by the denominator


(-10t)+(-15t)+4*50t^2=0

Wy multiply elements

200t^2+(-10t)+(-15t)=0

We get rid of parentheses

200t^2-10t-15t=0

We add all the numbers together, and all the variables

200t^2-25t=0

a = 200; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·200·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*200}=\frac{0}{400}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*200}=\frac{50}{400}
=1/8
$