20x*x=15200*20+1

Solution for 20x*x=15200*20+1 equation:

20x*x=15200*20+1

We move all terms to the left:

20x*x-(15200*20+1)=0

We add all the numbers together, and all the variables

20x*x-304001=0

Wy multiply elements

20x^2-304001=0

a = 20; b = 0; c = -304001;
Δ = b2-4ac
Δ = 02-4·20·(-304001)
Δ = 24320080
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:

$\sqrt{\Delta}=\sqrt{24320080}=\sqrt{16*1520005}=\sqrt{16}*\sqrt{1520005}=4\sqrt{1520005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{1520005}}{2*20}=\frac{0-4\sqrt{1520005}}{40}
=-\frac{4\sqrt{1520005}}{40}
=-\frac{\sqrt{1520005}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{1520005}}{2*20}=\frac{0+4\sqrt{1520005}}{40}
=\frac{4\sqrt{1520005}}{40}
=\frac{\sqrt{1520005}}{10}
$