-1/4x-3=x+7

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Solution for -1/4x-3=x+7 equation:



-1/4x-3=x+7
We move all terms to the left:
-1/4x-3-(x+7)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We get rid of parentheses
-1/4x-x-7-3=0
We multiply all the terms by the denominator
-x*4x-7*4x-3*4x-1=0
Wy multiply elements
-4x^2-28x-12x-1=0
We add all the numbers together, and all the variables
-4x^2-40x-1=0
a = -4; b = -40; c = -1;
Δ = b2-4ac
Δ = -402-4·(-4)·(-1)
Δ = 1584
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:
$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-12\sqrt{11}}{2*-4}=\frac{40-12\sqrt{11}}{-8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+12\sqrt{11}}{2*-4}=\frac{40+12\sqrt{11}}{-8} $

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