(7/8)t+(5/6)t=82

Solution for (7/8)t+(5/6)t=82 equation:

(7/8)t+(5/6)t=82

We move all terms to the left:

(7/8)t+(5/6)t-(82)=0


Domain of the equation: 8)t!=0

t!=0/1

t!=0

t∈R



Domain of the equation: 6)t!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

(+7/8)t+(+5/6)t-82=0

We multiply parentheses

7t^2+5t^2-82=0

We add all the numbers together, and all the variables

12t^2-82=0

a = 12; b = 0; c = -82;
Δ = b2-4ac
Δ = 02-4·12·(-82)
Δ = 3936
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:

$\sqrt{\Delta}=\sqrt{3936}=\sqrt{16*246}=\sqrt{16}*\sqrt{246}=4\sqrt{246}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{246}}{2*12}=\frac{0-4\sqrt{246}}{24}
=-\frac{4\sqrt{246}}{24}
=-\frac{\sqrt{246}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{246}}{2*12}=\frac{0+4\sqrt{246}}{24}
=\frac{4\sqrt{246}}{24}
=\frac{\sqrt{246}}{6}
$