(1+x)(3+x)=9,5x+18

Solution for (1+x)(3+x)=9,5x+18 equation:

(1+x)(3+x)=9.5x+18

We move all terms to the left:

(1+x)(3+x)-(9.5x+18)=0

We add all the numbers together, and all the variables

(x+1)(x+3)-(9.5x+18)=0

We get rid of parentheses

(x+1)(x+3)-9.5x-18=0

We multiply parentheses ..

(+x^2+3x+x+3)-9.5x-18=0

We get rid of parentheses

x^2+3x+x-9.5x+3-18=0

We add all the numbers together, and all the variables

x^2-5.5x-15=0

a = 1; b = -5.5; c = -15;
Δ = b2-4ac
Δ = -5.52-4·1·(-15)
Δ = 90.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5.5)-\sqrt{90.25}}{2*1}=\frac{5.5-\sqrt{90.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.5)+\sqrt{90.25}}{2*1}=\frac{5.5+\sqrt{90.25}}{2}
$