(2x+7)(x+5)=14

Solution for (2x+7)(x+5)=14 equation:

(2x+7)(x+5)=14

We move all terms to the left:

(2x+7)(x+5)-(14)=0

We multiply parentheses ..

(+2x^2+10x+7x+35)-14=0

We get rid of parentheses

2x^2+10x+7x+35-14=0

We add all the numbers together, and all the variables

2x^2+17x+21=0

a = 2; b = 17; c = +21;
Δ = b2-4ac
Δ = 172-4·2·21
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-11}{2*2}=\frac{-28}{4}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+11}{2*2}=\frac{-6}{4}
=-1+1/2
$