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

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



(3)/(4)x+3=(5)/(8)x+4
We move all terms to the left:
(3)/(4)x+3-((5)/(8)x+4)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 8x+4)!=0
x∈R
We get rid of parentheses
3/4x-5/8x-4+3=0
We calculate fractions
24x/32x^2+(-20x)/32x^2-4+3=0
We add all the numbers together, and all the variables
24x/32x^2+(-20x)/32x^2-1=0
We multiply all the terms by the denominator
24x+(-20x)-1*32x^2=0
Wy multiply elements
-32x^2+24x+(-20x)=0
We get rid of parentheses
-32x^2+24x-20x=0
We add all the numbers together, and all the variables
-32x^2+4x=0
a = -32; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-32)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-32}=\frac{-8}{-64} =1/8 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-32}=\frac{0}{-64} =0 $

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