3t-6=3/4t

Solution for 3t-6=3/4t equation:

3t-6=3/4t

We move all terms to the left:

3t-6-(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-(+3/4t)-6=0

We get rid of parentheses

3t-3/4t-6=0

We multiply all the terms by the denominator


3t*4t-6*4t-3=0

Wy multiply elements

12t^2-24t-3=0

a = 12; b = -24; c = -3;
Δ = b2-4ac
Δ = -242-4·12·(-3)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{5}}{2*12}=\frac{24-12\sqrt{5}}{24}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{5}}{2*12}=\frac{24+12\sqrt{5}}{24}
$