1/4a*2+4=2a

Solution for 1/4a*2+4=2a equation:

1/4a*2+4=2a

We move all terms to the left:

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


Domain of the equation: 4a*2!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-16a^2*2+32a*2+1=0

Wy multiply elements

-32a^2+64a+1=0

a = -32; b = 64; c = +1;
Δ = b2-4ac
Δ = 642-4·(-32)·1
Δ = 4224
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:

$\sqrt{\Delta}=\sqrt{4224}=\sqrt{64*66}=\sqrt{64}*\sqrt{66}=8\sqrt{66}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-8\sqrt{66}}{2*-32}=\frac{-64-8\sqrt{66}}{-64}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+8\sqrt{66}}{2*-32}=\frac{-64+8\sqrt{66}}{-64}
$