6(1/2a-3)-1/2a=5/2a-18

Solution for 6(1/2a-3)-1/2a=5/2a-18 equation:

6(1/2a-3)-1/2a=5/2a-18

We move all terms to the left:

6(1/2a-3)-1/2a-(5/2a-18)=0


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

a∈R



Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 2a-18)!=0

a∈R


We multiply parentheses

6a-1/2a-(5/2a-18)-18=0

We get rid of parentheses

6a-1/2a-5/2a+18-18=0

We multiply all the terms by the denominator


6a*2a+18*2a-18*2a-1-5=0

We add all the numbers together, and all the variables

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

Wy multiply elements

12a^2+36a-36a-6=0

We add all the numbers together, and all the variables

12a^2-6=0

a = 12; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·12·(-6)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*12}=\frac{0-12\sqrt{2}}{24}
=-\frac{12\sqrt{2}}{24}
=-\frac{\sqrt{2}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*12}=\frac{0+12\sqrt{2}}{24}
=\frac{12\sqrt{2}}{24}
=\frac{\sqrt{2}}{2}
$