3t-18=4(-3-3/2t)

Solution for 3t-18=4(-3-3/2t) equation:

3t-18=4(-3-3/2t)

We move all terms to the left:

3t-18-(4(-3-3/2t))=0


Domain of the equation: 2t))!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

3t-(4(-3/2t-3))-18=0

We multiply all the terms by the denominator


3t*2t-18*2t-3-3))-(4(-3))=0

We add all the numbers together, and all the variables

3t*2t-18*2t=0

Wy multiply elements

6t^2-36t=0

a = 6; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·6·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*6}=\frac{0}{12}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*6}=\frac{72}{12}
=6
$