x(x+6)=173.25

Solution for x(x+6)=173.25 equation:

x(x+6)=173.25

We move all terms to the left:

x(x+6)-(173.25)=0

We add all the numbers together, and all the variables

x(x+6)-173.25=0

We multiply parentheses

x^2+6x-173.25=0

a = 1; b = 6; c = -173.25;
Δ = b2-4ac
Δ = 62-4·1·(-173.25)
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{-(6)-27}{2*1}=\frac{-33}{2}
=-16+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+27}{2*1}=\frac{21}{2}
=10+1/2
$