(2x-23)(x+2)=0

Solution for (2x-23)(x+2)=0 equation:

(2x-23)(x+2)=0

We multiply parentheses ..

(+2x^2+4x-23x-46)=0

We get rid of parentheses

2x^2+4x-23x-46=0

We add all the numbers together, and all the variables

2x^2-19x-46=0

a = 2; b = -19; c = -46;
Δ = b2-4ac
Δ = -192-4·2·(-46)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-27}{2*2}=\frac{-8}{4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+27}{2*2}=\frac{46}{4}
=11+1/2
$