(1/4)9x-5=32x+8

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Solution for (1/4)9x-5=32x+8 equation:



(1/4)9x-5=32x+8
We move all terms to the left:
(1/4)9x-5-(32x+8)=0
Domain of the equation: 4)9x!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+1/4)9x-(32x+8)-5=0
We multiply parentheses
9x^2-(32x+8)-5=0
We get rid of parentheses
9x^2-32x-8-5=0
We add all the numbers together, and all the variables
9x^2-32x-13=0
a = 9; b = -32; c = -13;
Δ = b2-4ac
Δ = -322-4·9·(-13)
Δ = 1492
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:
$\sqrt{\Delta}=\sqrt{1492}=\sqrt{4*373}=\sqrt{4}*\sqrt{373}=2\sqrt{373}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{373}}{2*9}=\frac{32-2\sqrt{373}}{18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{373}}{2*9}=\frac{32+2\sqrt{373}}{18} $

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