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3t-18=4(-3-(3)/(4)t)
We move all terms to the left:
3t-18-(4(-3-(3)/(4)t))=0
Domain of the equation: 4t))!=0We add all the numbers together, and all the variables
t!=0/1
t!=0
t∈R
3t-(4(-3/4t-3))-18=0
We multiply all the terms by the denominator
3t*4t-18*4t-3-3))-(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 $
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