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

Solution for 3t-8=4(-3-3/4t) equation:

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

We move all terms to the left:

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


Domain of the equation: 4t))!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


3t*4t-8*4t-3-3))-(4(-3))=0

We add all the numbers together, and all the variables

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

Wy multiply elements

12t^2-32t=0

a = 12; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·12·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*12}=\frac{0}{24}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*12}=\frac{64}{24}
=2+2/3
$