(3x+23)(2x+17)=110

Solution for (3x+23)(2x+17)=110 equation:

(3x+23)(2x+17)=110

We move all terms to the left:

(3x+23)(2x+17)-(110)=0

We multiply parentheses ..

(+6x^2+51x+46x+391)-110=0

We get rid of parentheses

6x^2+51x+46x+391-110=0

We add all the numbers together, and all the variables

6x^2+97x+281=0

a = 6; b = 97; c = +281;
Δ = b2-4ac
Δ = 972-4·6·281
Δ = 2665
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{-(97)-\sqrt{2665}}{2*6}=\frac{-97-\sqrt{2665}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(97)+\sqrt{2665}}{2*6}=\frac{-97+\sqrt{2665}}{12}
$