-x2+4x+33=0

Solution for -x2+4x+33=0 equation:

-x2+4x+33=0

We add all the numbers together, and all the variables

-1x^2+4x+33=0

a = -1; b = 4; c = +33;
Δ = b2-4ac
Δ = 42-4·(-1)·33
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{37}}{2*-1}=\frac{-4-2\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{37}}{2*-1}=\frac{-4+2\sqrt{37}}{-2}
$