7/8x-30/107x=20900

Solution for 7/8x-30/107x=20900 equation:

7/8x-30/107x=20900

We move all terms to the left:

7/8x-30/107x-(20900)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 107x!=0

x!=0/107

x!=0

x∈R


We calculate fractions


749x/856x^2+(-240x)/856x^2-20900=0

We multiply all the terms by the denominator


749x+(-240x)-20900*856x^2=0

Wy multiply elements

-17890400x^2+749x+(-240x)=0

We get rid of parentheses

-17890400x^2+749x-240x=0

We add all the numbers together, and all the variables

-17890400x^2+509x=0

a = -17890400; b = 509; c = 0;
Δ = b2-4ac
Δ = 5092-4·(-17890400)·0
Δ = 259081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{259081}=509$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(509)-509}{2*-17890400}=\frac{-1018}{-35780800}
=509/17890400
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(509)+509}{2*-17890400}=\frac{0}{-35780800}
=0
$