8x(9x-6)-37x+x2+18=72

Solution for 8x(9x-6)-37x+x2+18=72 equation:

8x(9x-6)-37x+x2+18=72

We move all terms to the left:

8x(9x-6)-37x+x2+18-(72)=0

We add all the numbers together, and all the variables

x^2-37x+8x(9x-6)-54=0

We multiply parentheses

x^2+72x^2-37x-48x-54=0

We add all the numbers together, and all the variables

73x^2-85x-54=0

a = 73; b = -85; c = -54;
Δ = b2-4ac
Δ = -852-4·73·(-54)
Δ = 22993
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-\sqrt{22993}}{2*73}=\frac{85-\sqrt{22993}}{146}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+\sqrt{22993}}{2*73}=\frac{85+\sqrt{22993}}{146}
$