X2-20x2+85=0

Solution for X2-20x2+85=0 equation:

X2-20X^2+85=0

We add all the numbers together, and all the variables

-19X^2+85=0

a = -19; b = 0; c = +85;
Δ = b2-4ac
Δ = 02-4·(-19)·85
Δ = 6460
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:

$\sqrt{\Delta}=\sqrt{6460}=\sqrt{4*1615}=\sqrt{4}*\sqrt{1615}=2\sqrt{1615}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1615}}{2*-19}=\frac{0-2\sqrt{1615}}{-38}
=-\frac{2\sqrt{1615}}{-38}
=-\frac{\sqrt{1615}}{-19}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1615}}{2*-19}=\frac{0+2\sqrt{1615}}{-38}
=\frac{2\sqrt{1615}}{-38}
=\frac{\sqrt{1615}}{-19}
$