x/7x+5=16x

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Solution for x/7x+5=16x equation:



x/7x+5=16x
We move all terms to the left:
x/7x+5-(16x)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
We add all the numbers together, and all the variables
-16x+x/7x+5=0
We multiply all the terms by the denominator
-16x*7x+x+5*7x=0
We add all the numbers together, and all the variables
x-16x*7x+5*7x=0
Wy multiply elements
-112x^2+x+35x=0
We add all the numbers together, and all the variables
-112x^2+36x=0
a = -112; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-112)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-112}=\frac{-72}{-224} =9/28 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-112}=\frac{0}{-224} =0 $

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