4x^2-6x-23=0

Solution for 4x^2-6x-23=0 equation:

4x^2-6x-23=0

a = 4; b = -6; c = -23;
Δ = b2-4ac
Δ = -62-4·4·(-23)
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{101}}{2*4}=\frac{6-2\sqrt{101}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{101}}{2*4}=\frac{6+2\sqrt{101}}{8}
$