4x+1/7x=4.85714285714

Solution for 4x+1/7x=4.85714285714 equation:

4x+1/7x=4.85714285714

We move all terms to the left:

4x+1/7x-(4.85714285714)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/7x-4.85714285714=0

We multiply all the terms by the denominator


4x*7x-(4.85714285714)*7x+1=0

We multiply parentheses

4x*7x-33.99999999998x+1=0

Wy multiply elements

28x^2-33.99999999998x+1=0

a = 28; b = -33.99999999998; c = +1;
Δ = b2-4ac
Δ = -33.999999999982-4·28·1
Δ = 1043.9999999986
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{-(-33.99999999998)-\sqrt{1043.9999999986}}{2*28}=\frac{33.99999999998-\sqrt{1043.9999999986}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33.99999999998)+\sqrt{1043.9999999986}}{2*28}=\frac{33.99999999998+\sqrt{1043.9999999986}}{56}
$