3(2a-1)=3/4a-17

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Solution for 3(2a-1)=3/4a-17 equation:



3(2a-1)=3/4a-17
We move all terms to the left:
3(2a-1)-(3/4a-17)=0
Domain of the equation: 4a-17)!=0
a∈R
We multiply parentheses
6a-(3/4a-17)-3=0
We get rid of parentheses
6a-3/4a+17-3=0
We multiply all the terms by the denominator
6a*4a+17*4a-3*4a-3=0
Wy multiply elements
24a^2+68a-12a-3=0
We add all the numbers together, and all the variables
24a^2+56a-3=0
a = 24; b = 56; c = -3;
Δ = b2-4ac
Δ = 562-4·24·(-3)
Δ = 3424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{3424}=\sqrt{16*214}=\sqrt{16}*\sqrt{214}=4\sqrt{214}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{214}}{2*24}=\frac{-56-4\sqrt{214}}{48} $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{214}}{2*24}=\frac{-56+4\sqrt{214}}{48} $

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