40/t-16t=26

Solution for 40/t-16t=26 equation:

40/t-16t=26

We move all terms to the left:

40/t-16t-(26)=0


Domain of the equation: t!=0

t∈R


We add all the numbers together, and all the variables

-16t+40/t-26=0

We multiply all the terms by the denominator


-16t*t-26*t+40=0

We add all the numbers together, and all the variables

-26t-16t*t+40=0

Wy multiply elements

-16t^2-26t+40=0

a = -16; b = -26; c = +40;
Δ = b2-4ac
Δ = -262-4·(-16)·40
Δ = 3236
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:

$\sqrt{\Delta}=\sqrt{3236}=\sqrt{4*809}=\sqrt{4}*\sqrt{809}=2\sqrt{809}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{809}}{2*-16}=\frac{26-2\sqrt{809}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{809}}{2*-16}=\frac{26+2\sqrt{809}}{-32}
$