14x/5x+16=x/4

Solution for 14x/5x+16=x/4 equation:

14x/5x+16=x/4

We move all terms to the left:

14x/5x+16-(x/4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

14x/5x-(+x/4)+16=0

We get rid of parentheses

14x/5x-x/4+16=0

We calculate fractions


(-5x^2)/20x+56x/20x+16=0

We multiply all the terms by the denominator


(-5x^2)+56x+16*20x=0

Wy multiply elements

(-5x^2)+56x+320x=0

We get rid of parentheses

-5x^2+56x+320x=0

We add all the numbers together, and all the variables

-5x^2+376x=0

a = -5; b = 376; c = 0;
Δ = b2-4ac
Δ = 3762-4·(-5)·0
Δ = 141376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{141376}=376$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(376)-376}{2*-5}=\frac{-752}{-10}
=75+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(376)+376}{2*-5}=\frac{0}{-10}
=0
$