3/2t-16+16=4/3t-6+16

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Solution for 3/2t-16+16=4/3t-6+16 equation:



3/2t-16+16=4/3t-6+16
We move all terms to the left:
3/2t-16+16-(4/3t-6+16)=0
Domain of the equation: 2t!=0
t!=0/2
t!=0
t∈R
Domain of the equation: 3t-6+16)!=0
We move all terms containing t to the left, all other terms to the right
3t+16)!=6
t∈R
We add all the numbers together, and all the variables
3/2t-(4/3t+10)-16+16=0
We add all the numbers together, and all the variables
3/2t-(4/3t+10)=0
We get rid of parentheses
3/2t-4/3t-10=0
We calculate fractions
9t/6t^2+(-8t)/6t^2-10=0
We multiply all the terms by the denominator
9t+(-8t)-10*6t^2=0
Wy multiply elements
-60t^2+9t+(-8t)=0
We get rid of parentheses
-60t^2+9t-8t=0
We add all the numbers together, and all the variables
-60t^2+t=0
a = -60; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-60)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-60}=\frac{-2}{-120} =1/60 $
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-60}=\frac{0}{-120} =0 $

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