t/t-3-t-2/2=5t-3/4t-12

Solution for t/t-3-t-2/2=5t-3/4t-12 equation:

t/t-3-t-2/2=5t-3/4t-12

We move all terms to the left:

t/t-3-t-2/2-(5t-3/4t-12)=0


Domain of the equation: t!=0

t∈R



Domain of the equation: 4t-12)!=0

t∈R


We add all the numbers together, and all the variables

-1t+t/t-(5t-3/4t-12)-4=0

We get rid of parentheses

-1t+t/t-5t+3/4t+12-4=0

Fractions to decimals

3/4t-1t-5t+12-4+1=0

We multiply all the terms by the denominator


-1t*4t-5t*4t+12*4t-4*4t+1*4t+3=0

Wy multiply elements

-4t^2-20t^2+48t-16t+4t+3=0

We add all the numbers together, and all the variables

-24t^2+36t+3=0

a = -24; b = 36; c = +3;
Δ = b2-4ac
Δ = 362-4·(-24)·3
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{11}}{2*-24}=\frac{-36-12\sqrt{11}}{-48}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{11}}{2*-24}=\frac{-36+12\sqrt{11}}{-48}
$