1/8t+1/3t=10

Solution for 1/8t+1/3t=10 equation:

1/8t+1/3t=10

We move all terms to the left:

1/8t+1/3t-(10)=0


Domain of the equation: 8t!=0

t!=0/8

t!=0

t∈R



Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We calculate fractions


3t/24t^2+8t/24t^2-10=0

We multiply all the terms by the denominator


3t+8t-10*24t^2=0

We add all the numbers together, and all the variables

11t-10*24t^2=0

Wy multiply elements

-240t^2+11t=0

a = -240; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-240)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-240}=\frac{-22}{-480}
=11/240
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-240}=\frac{0}{-480}
=0
$