1/5t-4+2/5t=-6-1/10t

Solution for 1/5t-4+2/5t=-6-1/10t equation:

1/5t-4+2/5t=-6-1/10t

We move all terms to the left:

1/5t-4+2/5t-(-6-1/10t)=0


Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R



Domain of the equation: 10t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

1/5t+2/5t-(-1/10t-6)-4=0

We get rid of parentheses

1/5t+2/5t+1/10t+6-4=0

We calculate fractions


(20t+1)/50t^2+5t/50t^2+6-4=0

We add all the numbers together, and all the variables

(20t+1)/50t^2+5t/50t^2+2=0

We multiply all the terms by the denominator


(20t+1)+5t+2*50t^2=0

We add all the numbers together, and all the variables

5t+(20t+1)+2*50t^2=0

Wy multiply elements

100t^2+5t+(20t+1)=0

We get rid of parentheses

100t^2+5t+20t+1=0

We add all the numbers together, and all the variables

100t^2+25t+1=0

a = 100; b = 25; c = +1;
Δ = b2-4ac
Δ = 252-4·100·1
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-15}{2*100}=\frac{-40}{200}
=-1/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+15}{2*100}=\frac{-10}{200}
=-1/20
$