3/4t+7/8t=91

Solution for 3/4t+7/8t=91 equation:

3/4t+7/8t=91

We move all terms to the left:

3/4t+7/8t-(91)=0


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R



Domain of the equation: 8t!=0

t!=0/8

t!=0

t∈R


We calculate fractions


24t/32t^2+28t/32t^2-91=0

We multiply all the terms by the denominator


24t+28t-91*32t^2=0

We add all the numbers together, and all the variables

52t-91*32t^2=0

Wy multiply elements

-2912t^2+52t=0

a = -2912; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·(-2912)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*-2912}=\frac{-104}{-5824}
=1/56
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*-2912}=\frac{0}{-5824}
=0
$