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

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}
$