(2x+1)(x+1)=45

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Solution for (2x+1)(x+1)=45 equation: 



(2x+1)(x+1)=45

We move all terms to the left:

(2x+1)(x+1)-(45)=0

We multiply parentheses ..

(+2x^2+2x+x+1)-45=0

We get rid of parentheses

2x^2+2x+x+1-45=0

We add all the numbers together, and all the variables

2x^2+3x-44=0

a = 2; b = 3; c = -44;
Δ = b2-4ac
Δ = 32-4·2·(-44)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-19}{2*2}=\frac{-22}{4}
=-5+1/2
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+19}{2*2}=\frac{16}{4}
=4
$

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