180-15=2a+1/2a

Solution for 180-15=2a+1/2a equation:

180-15=2a+1/2a

We move all terms to the left:

180-15-(2a+1/2a)=0


Domain of the equation: 2a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

-(+2a+1/2a)+180-15=0

We add all the numbers together, and all the variables

-(+2a+1/2a)+165=0

We get rid of parentheses

-2a-1/2a+165=0

We multiply all the terms by the denominator


-2a*2a+165*2a-1=0

Wy multiply elements

-4a^2+330a-1=0

a = -4; b = 330; c = -1;
Δ = b2-4ac
Δ = 3302-4·(-4)·(-1)
Δ = 108884
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:

$\sqrt{\Delta}=\sqrt{108884}=\sqrt{4*27221}=\sqrt{4}*\sqrt{27221}=2\sqrt{27221}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(330)-2\sqrt{27221}}{2*-4}=\frac{-330-2\sqrt{27221}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(330)+2\sqrt{27221}}{2*-4}=\frac{-330+2\sqrt{27221}}{-8}
$