x^2-33x=-16

Solution for x^2-33x=-16 equation:

x^2-33x=-16

We move all terms to the left:

x^2-33x-(-16)=0

We add all the numbers together, and all the variables

x^2-33x+16=0

a = 1; b = -33; c = +16;
Δ = b2-4ac
Δ = -332-4·1·16
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-5\sqrt{41}}{2*1}=\frac{33-5\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+5\sqrt{41}}{2*1}=\frac{33+5\sqrt{41}}{2}
$