x+6x+(x^2+10)=180

Solution for x+6x+(x^2+10)=180 equation:

x+6x+(x^2+10)=180

We move all terms to the left:

x+6x+(x^2+10)-(180)=0

We add all the numbers together, and all the variables

7x+(x^2+10)-180=0

We get rid of parentheses

x^2+7x+10-180=0

We add all the numbers together, and all the variables

x^2+7x-170=0

a = 1; b = 7; c = -170;
Δ = b2-4ac
Δ = 72-4·1·(-170)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-27}{2*1}=\frac{-34}{2}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+27}{2*1}=\frac{20}{2}
=10
$