1/2x+3/4x=14

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Solution for 1/2x+3/4x=14 equation: 



1/2x+3/4x=14

We move all terms to the left:

1/2x+3/4x-(14)=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^2-14=0

We multiply all the terms by the denominator


4x+6x-14*8x^2=0

We add all the numbers together, and all the variables

10x-14*8x^2=0

Wy multiply elements

-112x^2+10x=0

a = -112; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-112)·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*-112}=\frac{-20}{-224}
=5/56
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-112}=\frac{0}{-224}
=0
$

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