4(2x-9)4x=4-6x

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Solution for 4(2x-9)4x=4-6x equation:



4(2x-9)4x=4-6x
We move all terms to the left:
4(2x-9)4x-(4-6x)=0
We add all the numbers together, and all the variables
4(2x-9)4x-(-6x+4)=0
We multiply parentheses
32x^2-144x-(-6x+4)=0
We get rid of parentheses
32x^2-144x+6x-4=0
We add all the numbers together, and all the variables
32x^2-138x-4=0
a = 32; b = -138; c = -4;
Δ = b2-4ac
Δ = -1382-4·32·(-4)
Δ = 19556
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{19556}=\sqrt{4*4889}=\sqrt{4}*\sqrt{4889}=2\sqrt{4889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-138)-2\sqrt{4889}}{2*32}=\frac{138-2\sqrt{4889}}{64} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-138)+2\sqrt{4889}}{2*32}=\frac{138+2\sqrt{4889}}{64} $

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