x+4x(5x+65)=180

Solution for x+4x(5x+65)=180 equation:

x+4x(5x+65)=180

We move all terms to the left:

x+4x(5x+65)-(180)=0

We multiply parentheses

20x^2+x+260x-180=0

We add all the numbers together, and all the variables

20x^2+261x-180=0

a = 20; b = 261; c = -180;
Δ = b2-4ac
Δ = 2612-4·20·(-180)
Δ = 82521
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:

$\sqrt{\Delta}=\sqrt{82521}=\sqrt{9*9169}=\sqrt{9}*\sqrt{9169}=3\sqrt{9169}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(261)-3\sqrt{9169}}{2*20}=\frac{-261-3\sqrt{9169}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(261)+3\sqrt{9169}}{2*20}=\frac{-261+3\sqrt{9169}}{40}
$