5x^2+8x-23=0

Solution for 5x^2+8x-23=0 equation:

5x^2+8x-23=0

a = 5; b = 8; c = -23;
Δ = b2-4ac
Δ = 82-4·5·(-23)
Δ = 524
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:

$\sqrt{\Delta}=\sqrt{524}=\sqrt{4*131}=\sqrt{4}*\sqrt{131}=2\sqrt{131}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{131}}{2*5}=\frac{-8-2\sqrt{131}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{131}}{2*5}=\frac{-8+2\sqrt{131}}{10}
$