-2/5t+1=3/10t-3

Solution for -2/5t+1=3/10t-3 equation:

-2/5t+1=3/10t-3

We move all terms to the left:

-2/5t+1-(3/10t-3)=0


Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R



Domain of the equation: 10t-3)!=0

t∈R


We get rid of parentheses

-2/5t-3/10t+3+1=0

We calculate fractions


(-20t)/50t^2+(-15t)/50t^2+3+1=0

We add all the numbers together, and all the variables

(-20t)/50t^2+(-15t)/50t^2+4=0

We multiply all the terms by the denominator


(-20t)+(-15t)+4*50t^2=0

Wy multiply elements

200t^2+(-20t)+(-15t)=0

We get rid of parentheses

200t^2-20t-15t=0

We add all the numbers together, and all the variables

200t^2-35t=0

a = 200; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·200·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*200}=\frac{0}{400}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*200}=\frac{70}{400}
=7/40
$