8a-24/4a-12=0

Solution for 8a-24/4a-12=0 equation:

8a-24/4a-12=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We multiply all the terms by the denominator


8a*4a-12*4a-24=0

Wy multiply elements

32a^2-48a-24=0

a = 32; b = -48; c = -24;
Δ = b2-4ac
Δ = -482-4·32·(-24)
Δ = 5376
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:

$\sqrt{\Delta}=\sqrt{5376}=\sqrt{256*21}=\sqrt{256}*\sqrt{21}=16\sqrt{21}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-16\sqrt{21}}{2*32}=\frac{48-16\sqrt{21}}{64}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+16\sqrt{21}}{2*32}=\frac{48+16\sqrt{21}}{64}
$