80=x(3x+1)

Solution for 80=x(3x+1) equation:

80=x(3x+1)

We move all terms to the left:

80-(x(3x+1))=0


We calculate terms in parentheses: -(x(3x+1)), so:

x(3x+1)

We multiply parentheses

3x^2+x

Back to the equation:

-(3x^2+x)


We get rid of parentheses

-3x^2-x+80=0

We add all the numbers together, and all the variables

-3x^2-1x+80=0

a = -3; b = -1; c = +80;
Δ = b2-4ac
Δ = -12-4·(-3)·80
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-31}{2*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+31}{2*-3}=\frac{32}{-6}
=-5+1/3
$