23x^2-208x-28=0

Solution for 23x^2-208x-28=0 equation:

23x^2-208x-28=0

a = 23; b = -208; c = -28;
Δ = b2-4ac
Δ = -2082-4·23·(-28)
Δ = 45840
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:

$\sqrt{\Delta}=\sqrt{45840}=\sqrt{16*2865}=\sqrt{16}*\sqrt{2865}=4\sqrt{2865}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-208)-4\sqrt{2865}}{2*23}=\frac{208-4\sqrt{2865}}{46}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-208)+4\sqrt{2865}}{2*23}=\frac{208+4\sqrt{2865}}{46}
$