1/2*6t-4=3t-2

Solution for 1/2*6t-4=3t-2 equation:

1/2*6t-4=3t-2

We move all terms to the left:

1/2*6t-4-(3t-2)=0


Domain of the equation: 2*6t!=0

t!=0/1

t!=0

t∈R


We get rid of parentheses

1/2*6t-3t+2-4=0

We multiply all the terms by the denominator


-3t*2*6t+2*2*6t-4*2*6t+1=0

Wy multiply elements

-36t^2*6+24t*6-48t*6+1=0

Wy multiply elements

-216t^2+144t-288t+1=0

We add all the numbers together, and all the variables

-216t^2-144t+1=0

a = -216; b = -144; c = +1;
Δ = b2-4ac
Δ = -1442-4·(-216)·1
Δ = 21600
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:

$\sqrt{\Delta}=\sqrt{21600}=\sqrt{3600*6}=\sqrt{3600}*\sqrt{6}=60\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-60\sqrt{6}}{2*-216}=\frac{144-60\sqrt{6}}{-432}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+60\sqrt{6}}{2*-216}=\frac{144+60\sqrt{6}}{-432}
$