3x(5x-20)+(x+20)=180

Solution for 3x(5x-20)+(x+20)=180 equation:

3x(5x-20)+(x+20)=180

We move all terms to the left:

3x(5x-20)+(x+20)-(180)=0

We multiply parentheses

15x^2-60x+(x+20)-180=0

We get rid of parentheses

15x^2-60x+x+20-180=0

We add all the numbers together, and all the variables

15x^2-59x-160=0

a = 15; b = -59; c = -160;
Δ = b2-4ac
Δ = -592-4·15·(-160)
Δ = 13081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-\sqrt{13081}}{2*15}=\frac{59-\sqrt{13081}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{13081}}{2*15}=\frac{59+\sqrt{13081}}{30}
$