14*x+(13+x)*x=238

Solution for 14*x+(13+x)*x=238 equation:

14x+(13+x)*x=238

We move all terms to the left:

14x+(13+x)*x-(238)=0

We add all the numbers together, and all the variables

14x+(x+13)*x-238=0

We multiply parentheses

x^2+14x+13x-238=0

We add all the numbers together, and all the variables

x^2+27x-238=0

a = 1; b = 27; c = -238;
Δ = b2-4ac
Δ = 272-4·1·(-238)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-41}{2*1}=\frac{-68}{2}
=-34
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+41}{2*1}=\frac{14}{2}
=7
$