3/4t-1=8t=

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

3/4t-1=8t=

We move all terms to the left:

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


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-8t*4t-1*4t+3=0

Wy multiply elements

-32t^2-4t+3=0

a = -32; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·(-32)·3
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-20}{2*-32}=\frac{-16}{-64}
=1/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+20}{2*-32}=\frac{24}{-64}
=-3/8
$