0=9x^2-137x+470

Solution for 0=9x^2-137x+470 equation:

0=9x^2-137x+470

We move all terms to the left:

0-(9x^2-137x+470)=0

We add all the numbers together, and all the variables

-(9x^2-137x+470)=0

We get rid of parentheses

-9x^2+137x-470=0

a = -9; b = 137; c = -470;
Δ = b2-4ac
Δ = 1372-4·(-9)·(-470)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(137)-43}{2*-9}=\frac{-180}{-18}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(137)+43}{2*-9}=\frac{-94}{-18}
=5+2/9
$