0=9x^2-89x+182

Solution for 0=9x^2-89x+182 equation:

0=9x^2-89x+182

We move all terms to the left:

0-(9x^2-89x+182)=0

We add all the numbers together, and all the variables

-(9x^2-89x+182)=0

We get rid of parentheses

-9x^2+89x-182=0

a = -9; b = 89; c = -182;
Δ = b2-4ac
Δ = 892-4·(-9)·(-182)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(89)-37}{2*-9}=\frac{-126}{-18}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(89)+37}{2*-9}=\frac{-52}{-18}
=2+8/9
$