3t-18=4(-3-13/4t)

Solution for 3t-18=4(-3-13/4t) equation:

3t-18=4(-3-13/4t)

We move all terms to the left:

3t-18-(4(-3-13/4t))=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(-13/4t-3))-18=0

We multiply all the terms by the denominator


3t*4t-18*4t-13-3))-(4(-3))=0

We add all the numbers together, and all the variables

3t*4t-18*4t=0

Wy multiply elements

12t^2-72t=0

a = 12; b = -72; c = 0;
Δ = b2-4ac
Δ = -722-4·12·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-72}{2*12}=\frac{0}{24}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+72}{2*12}=\frac{144}{24}
=6
$