0=9x^2-61x+80

Solution for 0=9x^2-61x+80 equation:

0=9x^2-61x+80

We move all terms to the left:

0-(9x^2-61x+80)=0

We add all the numbers together, and all the variables

-(9x^2-61x+80)=0

We get rid of parentheses

-9x^2+61x-80=0

a = -9; b = 61; c = -80;
Δ = b2-4ac
Δ = 612-4·(-9)·(-80)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-29}{2*-9}=\frac{-90}{-18}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+29}{2*-9}=\frac{-32}{-18}
=1+7/9
$