1/8t+3/4t-3=3

Solution for 1/8t+3/4t-3=3 equation:

1/8t+3/4t-3=3

We move all terms to the left:

1/8t+3/4t-3-(3)=0


Domain of the equation: 8t!=0

t!=0/8

t!=0

t∈R



Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R


We add all the numbers together, and all the variables

1/8t+3/4t-6=0

We calculate fractions


4t/32t^2+24t/32t^2-6=0

We multiply all the terms by the denominator


4t+24t-6*32t^2=0

We add all the numbers together, and all the variables

28t-6*32t^2=0

Wy multiply elements

-192t^2+28t=0

a = -192; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-192)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-192}=\frac{-56}{-384}
=7/48
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-192}=\frac{0}{-384}
=0
$