1/4x-3=1/2x+112

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Solution for 1/4x-3=1/2x+112 equation:



1/4x-3=1/2x+112
We move all terms to the left:
1/4x-3-(1/2x+112)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x+112)!=0
x∈R
We get rid of parentheses
1/4x-1/2x-112-3=0
We calculate fractions
2x/8x^2+(-4x)/8x^2-112-3=0
We add all the numbers together, and all the variables
2x/8x^2+(-4x)/8x^2-115=0
We multiply all the terms by the denominator
2x+(-4x)-115*8x^2=0
Wy multiply elements
-920x^2+2x+(-4x)=0
We get rid of parentheses
-920x^2+2x-4x=0
We add all the numbers together, and all the variables
-920x^2-2x=0
a = -920; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-920)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-920}=\frac{0}{-1840} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-920}=\frac{4}{-1840} =-1/460 $

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