x^2-9x=162

Solution for x^2-9x=162 equation:

x^2-9x=162

We move all terms to the left:

x^2-9x-(162)=0

a = 1; b = -9; c = -162;
Δ = b2-4ac
Δ = -92-4·1·(-162)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-27}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+27}{2*1}=\frac{36}{2}
=18
$