(2x+1)(x+7)=2x+14

Solution for (2x+1)(x+7)=2x+14 equation:

(2x+1)(x+7)=2x+14

We move all terms to the left:

(2x+1)(x+7)-(2x+14)=0

We get rid of parentheses

(2x+1)(x+7)-2x-14=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+13x-7=0

a = 2; b = 13; c = -7;
Δ = b2-4ac
Δ = 132-4·2·(-7)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-15}{2*2}=\frac{-28}{4}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+15}{2*2}=\frac{2}{4}
=1/2
$