3/4x-2=7/8x+2

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Solution for 3/4x-2=7/8x+2 equation:



3/4x-2=7/8x+2
We move all terms to the left:
3/4x-2-(7/8x+2)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 8x+2)!=0
x∈R
We get rid of parentheses
3/4x-7/8x-2-2=0
We calculate fractions
24x/32x^2+(-28x)/32x^2-2-2=0
We add all the numbers together, and all the variables
24x/32x^2+(-28x)/32x^2-4=0
We multiply all the terms by the denominator
24x+(-28x)-4*32x^2=0
Wy multiply elements
-128x^2+24x+(-28x)=0
We get rid of parentheses
-128x^2+24x-28x=0
We add all the numbers together, and all the variables
-128x^2-4x=0
a = -128; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-128)·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*-128}=\frac{0}{-256} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-128}=\frac{8}{-256} =-1/32 $

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