-31/3t+50=-5t+100

Solution for -31/3t+50=-5t+100 equation:

-31/3t+50=-5t+100

We move all terms to the left:

-31/3t+50-(-5t+100)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We get rid of parentheses

-31/3t+5t-100+50=0

We multiply all the terms by the denominator


5t*3t-100*3t+50*3t-31=0

Wy multiply elements

15t^2-300t+150t-31=0

We add all the numbers together, and all the variables

15t^2-150t-31=0

a = 15; b = -150; c = -31;
Δ = b2-4ac
Δ = -1502-4·15·(-31)
Δ = 24360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24360}=\sqrt{4*6090}=\sqrt{4}*\sqrt{6090}=2\sqrt{6090}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{6090}}{2*15}=\frac{150-2\sqrt{6090}}{30}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{6090}}{2*15}=\frac{150+2\sqrt{6090}}{30}
$