4x^2-17x-23=0

Solution for 4x^2-17x-23=0 equation:

4x^2-17x-23=0

a = 4; b = -17; c = -23;
Δ = b2-4ac
Δ = -172-4·4·(-23)
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3\sqrt{73}}{2*4}=\frac{17-3\sqrt{73}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3\sqrt{73}}{2*4}=\frac{17+3\sqrt{73}}{8}
$