(x+9)7x+x=180

Solution for (x+9)7x+x=180 equation:

(x+9)7x+x=180

We move all terms to the left:

(x+9)7x+x-(180)=0

We add all the numbers together, and all the variables

x+(x+9)7x-180=0

We multiply parentheses

7x^2+x+63x-180=0

We add all the numbers together, and all the variables

7x^2+64x-180=0

a = 7; b = 64; c = -180;
Δ = b2-4ac
Δ = 642-4·7·(-180)
Δ = 9136
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:

$\sqrt{\Delta}=\sqrt{9136}=\sqrt{16*571}=\sqrt{16}*\sqrt{571}=4\sqrt{571}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-4\sqrt{571}}{2*7}=\frac{-64-4\sqrt{571}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+4\sqrt{571}}{2*7}=\frac{-64+4\sqrt{571}}{14}
$