(X+4)(2x+3)=6

Solution for (X+4)(2x+3)=6 equation:

(X+4)(2X+3)=6

We move all terms to the left:

(X+4)(2X+3)-(6)=0

We multiply parentheses ..

(+2X^2+3X+8X+12)-6=0

We get rid of parentheses

2X^2+3X+8X+12-6=0

We add all the numbers together, and all the variables

2X^2+11X+6=0

a = 2; b = 11; c = +6;
Δ = b2-4ac
Δ = 112-4·2·6
Δ = 73
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{-(11)-\sqrt{73}}{2*2}=\frac{-11-\sqrt{73}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{73}}{2*2}=\frac{-11+\sqrt{73}}{4}
$