(2x+23)(x+12)=14

Solution for (2x+23)(x+12)=14 equation:

(2x+23)(x+12)=14

We move all terms to the left:

(2x+23)(x+12)-(14)=0

We multiply parentheses ..

(+2x^2+24x+23x+276)-14=0

We get rid of parentheses

2x^2+24x+23x+276-14=0

We add all the numbers together, and all the variables

2x^2+47x+262=0

a = 2; b = 47; c = +262;
Δ = b2-4ac
Δ = 472-4·2·262
Δ = 113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-\sqrt{113}}{2*2}=\frac{-47-\sqrt{113}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+\sqrt{113}}{2*2}=\frac{-47+\sqrt{113}}{4}
$