x(3x-13)+57=180

Solution for x(3x-13)+57=180 equation:

x(3x-13)+57=180

We move all terms to the left:

x(3x-13)+57-(180)=0

We add all the numbers together, and all the variables

x(3x-13)-123=0

We multiply parentheses

3x^2-13x-123=0

a = 3; b = -13; c = -123;
Δ = b2-4ac
Δ = -132-4·3·(-123)
Δ = 1645
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{-(-13)-\sqrt{1645}}{2*3}=\frac{13-\sqrt{1645}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{1645}}{2*3}=\frac{13+\sqrt{1645}}{6}
$