1/4x+32=x+11

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Solution for 1/4x+32=x+11 equation:



1/4x+32=x+11
We move all terms to the left:
1/4x+32-(x+11)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We get rid of parentheses
1/4x-x-11+32=0
We multiply all the terms by the denominator
-x*4x-11*4x+32*4x+1=0
Wy multiply elements
-4x^2-44x+128x+1=0
We add all the numbers together, and all the variables
-4x^2+84x+1=0
a = -4; b = 84; c = +1;
Δ = b2-4ac
Δ = 842-4·(-4)·1
Δ = 7072
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:
$\sqrt{\Delta}=\sqrt{7072}=\sqrt{16*442}=\sqrt{16}*\sqrt{442}=4\sqrt{442}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{442}}{2*-4}=\frac{-84-4\sqrt{442}}{-8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{442}}{2*-4}=\frac{-84+4\sqrt{442}}{-8} $

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