13x+2+x^2+x=270

Solution for 13x+2+x^2+x=270 equation:

13x+2+x^2+x=270

We move all terms to the left:

13x+2+x^2+x-(270)=0

We add all the numbers together, and all the variables

x^2+14x-268=0

a = 1; b = 14; c = -268;
Δ = b2-4ac
Δ = 142-4·1·(-268)
Δ = 1268
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1268}=\sqrt{4*317}=\sqrt{4}*\sqrt{317}=2\sqrt{317}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{317}}{2*1}=\frac{-14-2\sqrt{317}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{317}}{2*1}=\frac{-14+2\sqrt{317}}{2}
$