6.4a-12=1/4a-9

Solution for 6.4a-12=1/4a-9 equation:

6.4a-12=1/4a-9

We move all terms to the left:

6.4a-12-(1/4a-9)=0


Domain of the equation: 4a-9)!=0

a∈R


We get rid of parentheses

6.4a-1/4a+9-12=0

We multiply all the terms by the denominator


(6.4a)*4a+9*4a-12*4a-1=0

We add all the numbers together, and all the variables

(+6.4a)*4a+9*4a-12*4a-1=0

We multiply parentheses

24a^2+9*4a-12*4a-1=0

Wy multiply elements

24a^2+36a-48a-1=0

We add all the numbers together, and all the variables

24a^2-12a-1=0

a = 24; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·24·(-1)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*24}=\frac{12-4\sqrt{15}}{48}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*24}=\frac{12+4\sqrt{15}}{48}
$