14/x+5+7=4x+1

Solution for 14/x+5+7=4x+1 equation:

14/x+5+7=4x+1

We move all terms to the left:

14/x+5+7-(4x+1)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

14/x-(4x+1)+12=0

We get rid of parentheses

14/x-4x-1+12=0

We multiply all the terms by the denominator


-4x*x-1*x+12*x+14=0

We add all the numbers together, and all the variables

11x-4x*x+14=0

Wy multiply elements

-4x^2+11x+14=0

a = -4; b = 11; c = +14;
Δ = b2-4ac
Δ = 112-4·(-4)·14
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{345}}{2*-4}=\frac{-11-\sqrt{345}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{345}}{2*-4}=\frac{-11+\sqrt{345}}{-8}
$