-1/2a+6=2a-4

Solution for -1/2a+6=2a-4 equation:

-1/2a+6=2a-4

We move all terms to the left:

-1/2a+6-(2a-4)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We get rid of parentheses

-1/2a-2a+4+6=0

We multiply all the terms by the denominator


-2a*2a+4*2a+6*2a-1=0

Wy multiply elements

-4a^2+8a+12a-1=0

We add all the numbers together, and all the variables

-4a^2+20a-1=0

a = -4; b = 20; c = -1;
Δ = b2-4ac
Δ = 202-4·(-4)·(-1)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8\sqrt{6}}{2*-4}=\frac{-20-8\sqrt{6}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8\sqrt{6}}{2*-4}=\frac{-20+8\sqrt{6}}{-8}
$