(2x+1)(x+3)=117

Solution for (2x+1)(x+3)=117 equation:

(2x+1)(x+3)=117

We move all terms to the left:

(2x+1)(x+3)-(117)=0

We multiply parentheses ..

(+2x^2+6x+x+3)-117=0

We get rid of parentheses

2x^2+6x+x+3-117=0

We add all the numbers together, and all the variables

2x^2+7x-114=0

a = 2; b = 7; c = -114;
Δ = b2-4ac
Δ = 72-4·2·(-114)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-31}{2*2}=\frac{-38}{4}
=-9+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+31}{2*2}=\frac{24}{4}
=6
$