7/x-1/2=3/16x+5

Solution for 7/x-1/2=3/16x+5 equation:

7/x-1/2=3/16x+5

We move all terms to the left:

7/x-1/2-(3/16x+5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 16x+5)!=0

x∈R


We get rid of parentheses

7/x-3/16x-5-1/2=0

We calculate fractions


(-16x^2)/64x^2+448x/64x^2+(-12x)/64x^2-5=0

We multiply all the terms by the denominator


(-16x^2)+448x+(-12x)-5*64x^2=0

Wy multiply elements

(-16x^2)-320x^2+448x+(-12x)=0

We get rid of parentheses

-16x^2-320x^2+448x-12x=0

We add all the numbers together, and all the variables

-336x^2+436x=0

a = -336; b = 436; c = 0;
Δ = b2-4ac
Δ = 4362-4·(-336)·0
Δ = 190096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{190096}=436$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(436)-436}{2*-336}=\frac{-872}{-672}
=1+25/84
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(436)+436}{2*-336}=\frac{0}{-672}
=0
$