2x^2-33x=100=0

Solution for 2x^2-33x=100=0 equation:

2x^2-33x=100=0

We move all terms to the left:

2x^2-33x-(100)=0

a = 2; b = -33; c = -100;
Δ = b2-4ac
Δ = -332-4·2·(-100)
Δ = 1889
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{-(-33)-\sqrt{1889}}{2*2}=\frac{33-\sqrt{1889}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1889}}{2*2}=\frac{33+\sqrt{1889}}{4}
$