-.25x+6=2/3x+28

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Solution for -.25x+6=2/3x+28 equation:



-.25x+6=2/3x+28
We move all terms to the left:
-.25x+6-(2/3x+28)=0
Domain of the equation: 3x+28)!=0
x∈R
We add all the numbers together, and all the variables
-0.25x-(2/3x+28)+6=0
We get rid of parentheses
-0.25x-2/3x-28+6=0
We multiply all the terms by the denominator
-(0.25x)*3x-28*3x+6*3x-2=0
We add all the numbers together, and all the variables
-(+0.25x)*3x-28*3x+6*3x-2=0
We multiply parentheses
-0x^2-28*3x+6*3x-2=0
Wy multiply elements
-0x^2-84x+18x-2=0
We add all the numbers together, and all the variables
-1x^2-66x-2=0
a = -1; b = -66; c = -2;
Δ = b2-4ac
Δ = -662-4·(-1)·(-2)
Δ = 4348
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:
$\sqrt{\Delta}=\sqrt{4348}=\sqrt{4*1087}=\sqrt{4}*\sqrt{1087}=2\sqrt{1087}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1087}}{2*-1}=\frac{66-2\sqrt{1087}}{-2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1087}}{2*-1}=\frac{66+2\sqrt{1087}}{-2} $

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