6-3/4x+1/3=1/2x+15

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Solution for 6-3/4x+1/3=1/2x+15 equation:



6-3/4x+1/3=1/2x+15
We move all terms to the left:
6-3/4x+1/3-(1/2x+15)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x+15)!=0
x∈R
We get rid of parentheses
-3/4x-1/2x-15+6+1/3=0
We calculate fractions
16x^2/72x^2+(-54x)/72x^2+(-36x)/72x^2-15+6=0
We add all the numbers together, and all the variables
16x^2/72x^2+(-54x)/72x^2+(-36x)/72x^2-9=0
We multiply all the terms by the denominator
16x^2+(-54x)+(-36x)-9*72x^2=0
Wy multiply elements
16x^2-648x^2+(-54x)+(-36x)=0
We get rid of parentheses
16x^2-648x^2-54x-36x=0
We add all the numbers together, and all the variables
-632x^2-90x=0
a = -632; b = -90; c = 0;
Δ = b2-4ac
Δ = -902-4·(-632)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-90}{2*-632}=\frac{0}{-1264} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90}{2*-632}=\frac{180}{-1264} =-45/316 $

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