0.6x+7/4x+x=4014

Solution for 0.6x+7/4x+x=4014 equation:

0.6x+7/4x+x=4014

We move all terms to the left:

0.6x+7/4x+x-(4014)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1.6x+7/4x-4014=0

We multiply all the terms by the denominator


(1.6x)*4x-4014*4x+7=0

We add all the numbers together, and all the variables

(+1.6x)*4x-4014*4x+7=0

We multiply parentheses

4x^2-4014*4x+7=0

Wy multiply elements

4x^2-16056x+7=0

a = 4; b = -16056; c = +7;
Δ = b2-4ac
Δ = -160562-4·4·7
Δ = 257795024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{257795024}=\sqrt{16*16112189}=\sqrt{16}*\sqrt{16112189}=4\sqrt{16112189}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16056)-4\sqrt{16112189}}{2*4}=\frac{16056-4\sqrt{16112189}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16056)+4\sqrt{16112189}}{2*4}=\frac{16056+4\sqrt{16112189}}{8}
$