2x(2)-24x+33=0

Solution for 2x(2)-24x+33=0 equation:

2x(2)-24x+33=0

We add all the numbers together, and all the variables

2x^2-24x+33=0

a = 2; b = -24; c = +33;
Δ = b2-4ac
Δ = -242-4·2·33
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{78}}{2*2}=\frac{24-2\sqrt{78}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{78}}{2*2}=\frac{24+2\sqrt{78}}{4}
$