0=13x^2-80x+81

Solution for 0=13x^2-80x+81 equation:

0=13x^2-80x+81

We move all terms to the left:

0-(13x^2-80x+81)=0

We add all the numbers together, and all the variables

-(13x^2-80x+81)=0

We get rid of parentheses

-13x^2+80x-81=0

a = -13; b = 80; c = -81;
Δ = b2-4ac
Δ = 802-4·(-13)·(-81)
Δ = 2188
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:

$\sqrt{\Delta}=\sqrt{2188}=\sqrt{4*547}=\sqrt{4}*\sqrt{547}=2\sqrt{547}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-2\sqrt{547}}{2*-13}=\frac{-80-2\sqrt{547}}{-26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+2\sqrt{547}}{2*-13}=\frac{-80+2\sqrt{547}}{-26}
$