(2x+5)(2x+9)=14

Solution for (2x+5)(2x+9)=14 equation:

(2x+5)(2x+9)=14

We move all terms to the left:

(2x+5)(2x+9)-(14)=0

We multiply parentheses ..

(+4x^2+18x+10x+45)-14=0

We get rid of parentheses

4x^2+18x+10x+45-14=0

We add all the numbers together, and all the variables

4x^2+28x+31=0

a = 4; b = 28; c = +31;
Δ = b2-4ac
Δ = 282-4·4·31
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-12\sqrt{2}}{2*4}=\frac{-28-12\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+12\sqrt{2}}{2*4}=\frac{-28+12\sqrt{2}}{8}
$