x/7x+5=16x

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
$