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

7t-2t*t+25=0

Wy multiply elements

-2t^2+7t+25=0

a = -2; b = 7; c = +25;
Δ = b2-4ac
Δ = 72-4·(-2)·25
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{249}}{2*-2}=\frac{-7-\sqrt{249}}{-4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{249}}{2*-2}=\frac{-7+\sqrt{249}}{-4}
$