x^2-28x-37=0

Solution for x^2-28x-37=0 equation:

x^2-28x-37=0

a = 1; b = -28; c = -37;
Δ = b2-4ac
Δ = -282-4·1·(-37)
Δ = 932
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:

$\sqrt{\Delta}=\sqrt{932}=\sqrt{4*233}=\sqrt{4}*\sqrt{233}=2\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{233}}{2*1}=\frac{28-2\sqrt{233}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{233}}{2*1}=\frac{28+2\sqrt{233}}{2}
$