(3x+2)(x+5)=23

Solution for (3x+2)(x+5)=23 equation:

(3x+2)(x+5)=23

We move all terms to the left:

(3x+2)(x+5)-(23)=0

We multiply parentheses ..

(+3x^2+15x+2x+10)-23=0

We get rid of parentheses

3x^2+15x+2x+10-23=0

We add all the numbers together, and all the variables

3x^2+17x-13=0

a = 3; b = 17; c = -13;
Δ = b2-4ac
Δ = 172-4·3·(-13)
Δ = 445
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{-(17)-\sqrt{445}}{2*3}=\frac{-17-\sqrt{445}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{445}}{2*3}=\frac{-17+\sqrt{445}}{6}
$