x-9/20x=979

Solution for x-9/20x=979 equation:

x-9/20x=979

We move all terms to the left:

x-9/20x-(979)=0


Domain of the equation: 20x!=0

x!=0/20

x!=0

x∈R


We multiply all the terms by the denominator


x*20x-979*20x-9=0

Wy multiply elements

20x^2-19580x-9=0

a = 20; b = -19580; c = -9;
Δ = b2-4ac
Δ = -195802-4·20·(-9)
Δ = 383377120
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:

$\sqrt{\Delta}=\sqrt{383377120}=\sqrt{16*23961070}=\sqrt{16}*\sqrt{23961070}=4\sqrt{23961070}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19580)-4\sqrt{23961070}}{2*20}=\frac{19580-4\sqrt{23961070}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19580)+4\sqrt{23961070}}{2*20}=\frac{19580+4\sqrt{23961070}}{40}
$