25/t+6=2t+1

Solution for 25/t+6=2t+1 equation:

25/t+6=2t+1

We move all terms to the left:

25/t+6-(2t+1)=0


Domain of the equation: t!=0

t∈R


We get rid of parentheses

25/t-2t-1+6=0

We multiply all the terms by the denominator


-2t*t-1*t+6*t+25=0

We add all the numbers together, and all the variables

5t-2t*t+25=0

Wy multiply elements

-2t^2+5t+25=0

a = -2; b = 5; c = +25;
Δ = b2-4ac
Δ = 52-4·(-2)·25
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{-(5)-15}{2*-2}=\frac{-20}{-4}
=+5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+15}{2*-2}=\frac{10}{-4}
=-2+1/2
$