5/8x+3/4=4+3/4x

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Solution for 5/8x+3/4=4+3/4x equation:



5/8x+3/4=4+3/4x
We move all terms to the left:
5/8x+3/4-(4+3/4x)=0
Domain of the equation: 8x!=0
x!=0/8
x!=0
x∈R
Domain of the equation: 4x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
5/8x-(3/4x+4)+3/4=0
We get rid of parentheses
5/8x-3/4x-4+3/4=0
We calculate fractions
320x/512x^2+(-24x)/512x^2+24x/512x^2-4=0
We multiply all the terms by the denominator
320x+(-24x)+24x-4*512x^2=0
We add all the numbers together, and all the variables
344x+(-24x)-4*512x^2=0
Wy multiply elements
-2048x^2+344x+(-24x)=0
We get rid of parentheses
-2048x^2+344x-24x=0
We add all the numbers together, and all the variables
-2048x^2+320x=0
a = -2048; b = 320; c = 0;
Δ = b2-4ac
Δ = 3202-4·(-2048)·0
Δ = 102400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{102400}=320$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320)-320}{2*-2048}=\frac{-640}{-4096} =5/32 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320)+320}{2*-2048}=\frac{0}{-4096} =0 $

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