6(1/2a-3)-1/2a=0

Solution for 6(1/2a-3)-1/2a=0 equation:

6(1/2a-3)-1/2a=0


Domain of the equation: 2a-3)!=0

a∈R



Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We multiply parentheses

6a-1/2a-18=0

We multiply all the terms by the denominator


6a*2a-18*2a-1=0

Wy multiply elements

12a^2-36a-1=0

a = 12; b = -36; c = -1;
Δ = b2-4ac
Δ = -362-4·12·(-1)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{21}}{2*12}=\frac{36-8\sqrt{21}}{24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{21}}{2*12}=\frac{36+8\sqrt{21}}{24}
$