9x(X-8)+8x(x-9)=-212

Solution for 9x(X-8)+8x(x-9)=-212 equation:

9x(x-8)+8x(x-9)=-212

We move all terms to the left:

9x(x-8)+8x(x-9)-(-212)=0

We add all the numbers together, and all the variables

9x(x-8)+8x(x-9)+212=0

We multiply parentheses

9x^2+8x^2-72x-72x+212=0

We add all the numbers together, and all the variables

17x^2-144x+212=0

a = 17; b = -144; c = +212;
Δ = b2-4ac
Δ = -1442-4·17·212
Δ = 6320
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:

$\sqrt{\Delta}=\sqrt{6320}=\sqrt{16*395}=\sqrt{16}*\sqrt{395}=4\sqrt{395}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-4\sqrt{395}}{2*17}=\frac{144-4\sqrt{395}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+4\sqrt{395}}{2*17}=\frac{144+4\sqrt{395}}{34}
$