7831674183216438271+90/56*x=x+x*20

Solution for 7831674183216438271+90/56*x=x+x*20 equation:

7831674183216438271+90/56x=x+x*20

We move all terms to the left:

7831674183216438271+90/56x-(x+x*20)=0


Domain of the equation: 56x!=0

x!=0/56

x!=0

x∈R


We add all the numbers together, and all the variables

90/56x-(+x+x*20)+7831674183216438271=0

We get rid of parentheses

90/56x-x-x*20+7831674183216438271=0

We multiply all the terms by the denominator


-x*56x-(x*20)*56x+7831674183216438271*56x+90=0

We add all the numbers together, and all the variables

-x*56x-(+x*20)*56x+7831674183216438271*56x+90=0

We multiply parentheses

-1120x^2-x*56x+7831674183216438271*56x+90=0

Wy multiply elements

-1120x^2-56x^2+20x+90+4.3857375426012E=0

We add all the numbers together, and all the variables

-1176x^2+20x+101.92167066644=0

a = -1176; b = 20; c = +101.92167066644;
Δ = b2-4ac
Δ = 202-4·(-1176)·101.92167066644
Δ = 479839.53881493
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{-(20)-\sqrt{479839.53881493}}{2*-1176}=\frac{-20-\sqrt{479839.53881493}}{-2352}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+\sqrt{479839.53881493}}{2*-1176}=\frac{-20+\sqrt{479839.53881493}}{-2352}
$