x+3x(x-20)=52

Solution for x+3x(x-20)=52 equation:

x+3x(x-20)=52

We move all terms to the left:

x+3x(x-20)-(52)=0

We multiply parentheses

3x^2+x-60x-52=0

We add all the numbers together, and all the variables

3x^2-59x-52=0

a = 3; b = -59; c = -52;
Δ = b2-4ac
Δ = -592-4·3·(-52)
Δ = 4105
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{4105}}{2*3}=\frac{59-\sqrt{4105}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{4105}}{2*3}=\frac{59+\sqrt{4105}}{6}
$