1/2x+3/4x=1

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



1/2x+3/4x=1
We move all terms to the left:
1/2x+3/4x-(1)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We calculate fractions
4x/8x^2+6x/8x^2-1=0
We multiply all the terms by the denominator
4x+6x-1*8x^2=0
We add all the numbers together, and all the variables
10x-1*8x^2=0
Wy multiply elements
-8x^2+10x=0
a = -8; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-8)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-8}=\frac{-20}{-16} =1+1/4 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-8}=\frac{0}{-16} =0 $

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