7-21x/6*4x+10/14-42x=x

Solution for 7-21x/6*4x+10/14-42x=x equation:

7-21x/6*4x+10/14-42x=x

We move all terms to the left:

7-21x/6*4x+10/14-42x-(x)=0


Domain of the equation: 6*4x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-43x-21x/6*4x+7+10/14=0

We calculate fractions


-43x+(-294x)/336x+960x/336x+7=0

We multiply all the terms by the denominator


-43x*336x+(-294x)+960x+7*336x=0

We add all the numbers together, and all the variables

960x-43x*336x+(-294x)+7*336x=0

Wy multiply elements

-14448x^2+960x+(-294x)+2352x=0

We get rid of parentheses

-14448x^2+960x-294x+2352x=0

We add all the numbers together, and all the variables

-14448x^2+3018x=0

a = -14448; b = 3018; c = 0;
Δ = b2-4ac
Δ = 30182-4·(-14448)·0
Δ = 9108324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9108324}=3018$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3018)-3018}{2*-14448}=\frac{-6036}{-28896}
=503/2408
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3018)+3018}{2*-14448}=\frac{0}{-28896}
=0
$