x^2-18x^2+80=0

Solution for x^2-18x^2+80=0 equation:

x^2-18x^2+80=0

We add all the numbers together, and all the variables

-17x^2+80=0

a = -17; b = 0; c = +80;
Δ = b2-4ac
Δ = 02-4·(-17)·80
Δ = 5440
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:

$\sqrt{\Delta}=\sqrt{5440}=\sqrt{64*85}=\sqrt{64}*\sqrt{85}=8\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{85}}{2*-17}=\frac{0-8\sqrt{85}}{-34}
=-\frac{8\sqrt{85}}{-34}
=-\frac{4\sqrt{85}}{-17}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{85}}{2*-17}=\frac{0+8\sqrt{85}}{-34}
=\frac{8\sqrt{85}}{-34}
=\frac{4\sqrt{85}}{-17}
$