30(-2/5t+1)=(3/10t-3)30

Solution for 30(-2/5t+1)=(3/10t-3)30 equation:

30(-2/5t+1)=(3/10t-3)30

We move all terms to the left:

30(-2/5t+1)-((3/10t-3)30)=0


Domain of the equation: 5t+1)!=0

t∈R



Domain of the equation: 10t-3)30)!=0

t∈R


We multiply parentheses

-60t-((3/10t-3)30)+30=0

We multiply all the terms by the denominator


-60t*10t+30*10t-3)30)-((3-3)30)=0

We add all the numbers together, and all the variables

-60t*10t+30*10t-3)30)-(030)=0

We add all the numbers together, and all the variables

-60t*10t+30*10t=0

Wy multiply elements

-600t^2+300t=0

a = -600; b = 300; c = 0;
Δ = b2-4ac
Δ = 3002-4·(-600)·0
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-300}{2*-600}=\frac{-600}{-1200}
=1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+300}{2*-600}=\frac{0}{-1200}
=0
$