5/6t+7/8t=164

Solution for 5/6t+7/8t=164 equation:

5/6t+7/8t=164

We move all terms to the left:

5/6t+7/8t-(164)=0


Domain of the equation: 6t!=0

t!=0/6

t!=0

t∈R



Domain of the equation: 8t!=0

t!=0/8

t!=0

t∈R


We calculate fractions


40t/48t^2+42t/48t^2-164=0

We multiply all the terms by the denominator


40t+42t-164*48t^2=0

We add all the numbers together, and all the variables

82t-164*48t^2=0

Wy multiply elements

-7872t^2+82t=0

a = -7872; b = 82; c = 0;
Δ = b2-4ac
Δ = 822-4·(-7872)·0
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-82}{2*-7872}=\frac{-164}{-15744}
=1/96
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+82}{2*-7872}=\frac{0}{-15744}
=0
$