7x^2-28x-33=0

Solution for 7x^2-28x-33=0 equation:

7x^2-28x-33=0

a = 7; b = -28; c = -33;
Δ = b2-4ac
Δ = -282-4·7·(-33)
Δ = 1708
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:

$\sqrt{\Delta}=\sqrt{1708}=\sqrt{4*427}=\sqrt{4}*\sqrt{427}=2\sqrt{427}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{427}}{2*7}=\frac{28-2\sqrt{427}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{427}}{2*7}=\frac{28+2\sqrt{427}}{14}
$