5x^2-27x+182.25=200.25

Solution for 5x^2-27x+182.25=200.25 equation:

5x^2-27x+182.25=200.25

We move all terms to the left:

5x^2-27x+182.25-(200.25)=0

We add all the numbers together, and all the variables

5x^2-27x-18=0

a = 5; b = -27; c = -18;
Δ = b2-4ac
Δ = -272-4·5·(-18)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-33}{2*5}=\frac{-6}{10}
=-3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+33}{2*5}=\frac{60}{10}
=6
$